sequence_id stringlengths 7 7 | sequence_name stringlengths 4 573 | sequence listlengths 1 348 | keywords listlengths 1 7 | score int64 1 2.47k | offset_a int64 -14,827 666,262,453B | offset_b int64 0 635M ⌀ | cross_references listlengths 1 128 ⌀ | former_ids listlengths 1 3 ⌀ | author stringlengths 7 231 ⌀ | timestamp timestamp[us]date 1999-12-11 03:00:00 2026-01-19 02:46:49 | filename stringlengths 29 29 | hash stringlengths 32 32 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
A391325 | Expansion of g/(1 + x^2*g^3), where g = 1+x*g^4 is the g.f. of A002293. | [
"1",
"1",
"3",
"18",
"119",
"836",
"6163",
"47083",
"369523",
"2961771",
"24142264",
"199523492",
"1668022194",
"14080977404",
"119862325698",
"1027703841061",
"8867388886873",
"76938287369920",
"670870542856477",
"5875670906414555",
"51666127774874471",
"455951711256500829... | [
"nonn"
] | 14 | 0 | 3 | [
"A002293",
"A391099",
"A391325"
] | null | Seiichi Manyama, Dec 07 2025 | 2025-12-08T10:28:34 | oeisdata/seq/A391/A391325.seq | 2c204dbb5d307c62e69787ee1a0e46d1 |
A391326 | Expansion of g/(1 + x^3*g^3), where g = 1+x*g^4 is the g.f. of A002293. | [
"1",
"1",
"4",
"21",
"136",
"947",
"6945",
"52858",
"413697",
"3308796",
"26925841",
"222227383",
"1855755034",
"15651109359",
"133121828588",
"1140609311220",
"9835711615762",
"85295338371581",
"743396385161313",
"6508187266161161",
"57206828084607355",
"504679861263048121... | [
"nonn"
] | 13 | 0 | 3 | [
"A002293",
"A391100",
"A391326"
] | null | Seiichi Manyama, Dec 07 2025 | 2025-12-08T10:28:37 | oeisdata/seq/A391/A391326.seq | e9bee82cfaebf39da680b0424cbd9d1d |
A391327 | Expansion of g/(1 + x^2*g^6), where g = 1+x*g^4 is the g.f. of A002293. | [
"1",
"1",
"3",
"15",
"92",
"625",
"4518",
"34067",
"264876",
"2108122",
"17089955",
"140620685",
"1171370236",
"9858740030",
"83708026208",
"716151866019",
"6167531084156",
"53424291896860",
"465157370556204",
"4068682850990824",
"35735239228966952",
"315031802838535433",
... | [
"nonn"
] | 17 | 0 | 3 | [
"A002293",
"A387639",
"A391104",
"A391306",
"A391323",
"A391325",
"A391327"
] | null | Seiichi Manyama, Dec 07 2025 | 2025-12-08T10:28:41 | oeisdata/seq/A391/A391327.seq | 43ca061dd82f1f6e564ef8cda02fab6f |
A391328 | Odd semiprimes k = p*q, p, q primes > 3, such that either k = A048720(p,x) or k = A048720(q,x) for some x, where A048720 is the carryless binary multiplication. | [
"35",
"49",
"65",
"85",
"95",
"119",
"133",
"155",
"161",
"187",
"215",
"217",
"221",
"235",
"259",
"287",
"335",
"341",
"365",
"371",
"403",
"413",
"427",
"469",
"485",
"497",
"511",
"527",
"589",
"611",
"629",
"635",
"655",
"679",
"685",
"689",... | [
"nonn",
"base"
] | 9 | 1 | 1 | [
"A001651",
"A048720",
"A391253",
"A391328",
"A391330",
"A391335"
] | null | Antti Karttunen, Dec 07 2025 | 2025-12-07T20:15:09 | oeisdata/seq/A391/A391328.seq | 855447522d469bb7c1db90b5cfcb54ef |
A391329 | Odd semiprimes p*q, p, q > 3, such that Stern polynomial B(p*q,x) is a multiple of either B(p,x) or B(q,x). | [
"35",
"49",
"85",
"119",
"155",
"187",
"217",
"221",
"259",
"287",
"341",
"355",
"365",
"371",
"403",
"413",
"437",
"497",
"511",
"527",
"535",
"553",
"565",
"589",
"611",
"635",
"685",
"713",
"745",
"791",
"793",
"835",
"871",
"889",
"899",
"901... | [
"nonn"
] | 10 | 1 | 1 | [
"A001651",
"A125184",
"A260443",
"A391257",
"A391329",
"A391330",
"A391336"
] | null | Antti Karttunen, Dec 08 2025 | 2025-12-14T12:01:44 | oeisdata/seq/A391/A391329.seq | a4c7a0aaf64ba3218104861b41107c58 |
A391330 | Odd semiprimes that are not multiples of 3; Semiprimes congruent to 1 or 5 mod 6. | [
"25",
"35",
"49",
"55",
"65",
"77",
"85",
"91",
"95",
"115",
"119",
"121",
"133",
"143",
"145",
"155",
"161",
"169",
"185",
"187",
"203",
"205",
"209",
"215",
"217",
"221",
"235",
"247",
"253",
"259",
"265",
"287",
"289",
"295",
"299",
"301",
"... | [
"nonn"
] | 24 | 1 | 1 | [
"A001358",
"A007310",
"A038509",
"A046315",
"A176551",
"A391328",
"A391329",
"A391330",
"A391331",
"A391334",
"A391335",
"A391337"
] | null | Antti Karttunen, Dec 07 2025 | 2025-12-09T16:43:43 | oeisdata/seq/A391/A391330.seq | b86d2faa382b9b055bb40da1acbd4224 |
A391331 | Odd semiprimes k = p*q such that k = A325820(p,q), with p, q primes > 3, and A325820 is the carryless base-3 multiplication. | [
"377",
"403",
"481",
"961",
"1079",
"1199",
"1355",
"1369",
"1417",
"1897",
"2071",
"2119",
"2573",
"3071",
"3379",
"3523",
"3695",
"3785",
"4033",
"4055",
"5053",
"5173",
"5299",
"5677",
"6031",
"6331",
"8063",
"8327",
"8401",
"9529",
"9607",
"9841",
... | [
"nonn",
"base"
] | 10 | 1 | 1 | [
"A001651",
"A007089",
"A325820",
"A391330",
"A391331",
"A391332",
"A391335"
] | null | Antti Karttunen, Dec 07 2025 | 2025-12-07T15:18:41 | oeisdata/seq/A391/A391331.seq | d9d9391b98df3ddf29689fa33581108e |
A391332 | Odd semiprimes k = p*q such that k = A325820(p,q), with p, q primes, where A325820 is the carryless base-3 multiplication. | [
"9",
"15",
"21",
"33",
"39",
"51",
"57",
"69",
"87",
"93",
"111",
"123",
"129",
"141",
"159",
"177",
"183",
"201",
"213",
"219",
"237",
"249",
"267",
"291",
"303",
"309",
"321",
"327",
"339",
"377",
"381",
"393",
"403",
"411",
"417",
"447",
"45... | [
"nonn",
"base"
] | 9 | 1 | 1 | [
"A001748",
"A325820",
"A365473",
"A391331",
"A391332",
"A391333"
] | null | Antti Karttunen, Dec 07 2025 | 2025-12-07T15:18:54 | oeisdata/seq/A391/A391332.seq | f635466179010fae177c0512eb6d9658 |
A391333 | Odd semiprimes k = p*q, with p, q primes, such that either k = A325820(p,x) or k = A325820(q,x) for some x, where A325820 is the carryless base-3 multiplication. | [
"9",
"15",
"21",
"33",
"39",
"51",
"55",
"57",
"69",
"85",
"87",
"91",
"93",
"111",
"119",
"123",
"129",
"141",
"159",
"161",
"177",
"183",
"201",
"213",
"215",
"219",
"237",
"247",
"249",
"267",
"291",
"301",
"303",
"309",
"321",
"327",
"339",... | [
"nonn",
"base"
] | 11 | 1 | 1 | [
"A046315",
"A325820",
"A391253",
"A391332",
"A391333",
"A391334",
"A391335"
] | null | Antti Karttunen, Dec 07 2025 | 2025-12-07T15:19:07 | oeisdata/seq/A391/A391333.seq | c8e2f7fa2d6f6868c5092f22d573d151 |
A391334 | Odd semiprimes k = p*q, with p, q primes, such that neither k = A325820(p,x) nor k = A325820(q,x) for any x, where A325820 is the carryless base-3 multiplication. | [
"25",
"35",
"49",
"65",
"77",
"95",
"115",
"121",
"133",
"143",
"145",
"155",
"169",
"185",
"187",
"203",
"205",
"209",
"217",
"221",
"235",
"253",
"259",
"265",
"287",
"289",
"295",
"299",
"305",
"319",
"323",
"329",
"335",
"341",
"355",
"361",
... | [
"nonn",
"base"
] | 9 | 1 | 1 | [
"A046315",
"A325820",
"A391254",
"A391330",
"A391333",
"A391334"
] | null | Antti Karttunen, Dec 07 2025 | 2025-12-07T15:19:02 | oeisdata/seq/A391/A391334.seq | ebaea00c2539bd9fe75449396a3b94c0 |
A391335 | Odd semiprimes k = p*q, with p, q primes > 3, such that either k = A325820(p,x) or k = A325820(q,x) for some x, where A325820 is the carryless base-3 multiplication. | [
"55",
"85",
"91",
"119",
"161",
"215",
"247",
"301",
"371",
"377",
"395",
"403",
"481",
"553",
"565",
"611",
"635",
"671",
"689",
"695",
"707",
"721",
"799",
"817",
"889",
"917",
"959",
"961",
"965",
"973",
"1007",
"1043",
"1079",
"1099",
"1115",
... | [
"nonn",
"base"
] | 8 | 1 | 1 | [
"A001651",
"A325820",
"A391330",
"A391331",
"A391333",
"A391335"
] | null | Antti Karttunen, Dec 07 2025 | 2025-12-07T15:18:58 | oeisdata/seq/A391/A391335.seq | fc2c6a37b4aa1ee033d71bd835dc6688 |
A391336 | Odd semiprimes p*q such that Stern polynomial B(p*q,x) is reducible. | [
"9",
"15",
"21",
"33",
"35",
"39",
"49",
"51",
"57",
"69",
"85",
"87",
"93",
"111",
"119",
"123",
"129",
"141",
"155",
"159",
"177",
"183",
"187",
"201",
"213",
"217",
"219",
"221",
"237",
"249",
"259",
"267",
"287",
"291",
"303",
"309",
"321",... | [
"nonn"
] | 12 | 1 | 1 | [
"A046315",
"A125184",
"A260443",
"A389917",
"A389918",
"A391256",
"A391257",
"A391336",
"A391337"
] | null | Antti Karttunen, Dec 08 2025 | 2025-12-14T12:01:48 | oeisdata/seq/A391/A391336.seq | 11aeb8f1e78fa5343a2525121b18e074 |
A391337 | Odd semiprimes p*q, such that Stern polynomial B(p*q,x) is irreducible. | [
"25",
"55",
"65",
"77",
"91",
"95",
"115",
"121",
"133",
"143",
"145",
"161",
"169",
"185",
"203",
"205",
"209",
"215",
"235",
"247",
"253",
"265",
"289",
"295",
"299",
"301",
"305",
"319",
"323",
"329",
"335",
"361",
"377",
"391",
"395",
"407",
... | [
"nonn"
] | 20 | 1 | 1 | [
"A046315",
"A125184",
"A186891",
"A186892",
"A260443",
"A391258",
"A391330",
"A391336",
"A391337",
"A391338",
"A391339"
] | null | Antti Karttunen, Dec 08 2025 | 2025-12-14T14:02:41 | oeisdata/seq/A391/A391337.seq | 155751be65a19b0375f170d1ec56024d |
A391338 | Numbers k such that Stern polynomial B(3*k,x) is equal to B(3,x) * B(k,x). | [
"1",
"2",
"3",
"4",
"6",
"8",
"9",
"12",
"13",
"16",
"18",
"23",
"24",
"26",
"32",
"35",
"36",
"46",
"48",
"51",
"52",
"59",
"64",
"70",
"72",
"73",
"79",
"92",
"93",
"96",
"102",
"104",
"105",
"118",
"128",
"140",
"141",
"144",
"146",
"1... | [
"nonn"
] | 17 | 1 | 2 | [
"A125184",
"A260443",
"A391260",
"A391338",
"A391339",
"A391340",
"A391348"
] | null | Antti Karttunen, Dec 08 2025 | 2025-12-14T14:02:52 | oeisdata/seq/A391/A391338.seq | db96b2528dcc7451f1d16b6eb15decab |
A391339 | Numbers k such that Stern polynomial B(3*k,x) is not equal to B(3,x) * B(k,x). | [
"5",
"7",
"10",
"11",
"14",
"15",
"17",
"19",
"20",
"21",
"22",
"25",
"27",
"28",
"29",
"30",
"31",
"33",
"34",
"37",
"38",
"39",
"40",
"41",
"42",
"43",
"44",
"45",
"47",
"49",
"50",
"53",
"54",
"55",
"56",
"57",
"58",
"60",
"61",
"62",
... | [
"nonn"
] | 14 | 1 | 1 | [
"A125184",
"A260443",
"A391260",
"A391337",
"A391338",
"A391339",
"A391349"
] | null | Antti Karttunen, Dec 08 2025 | 2025-12-14T14:02:56 | oeisdata/seq/A391/A391339.seq | 7ef51d5dbfe6c5532efb428c698f9b98 |
A391340 | Odd numbers k such that Stern polynomial B(3*k,x) is equal to B(3,x) * B(k,x). | [
"1",
"3",
"9",
"13",
"23",
"35",
"51",
"59",
"73",
"79",
"93",
"105",
"141",
"183",
"205",
"279",
"291",
"371",
"407",
"419",
"563",
"585",
"733",
"745",
"819",
"841",
"1117",
"1129",
"1165",
"1311",
"1463",
"1485",
"1629",
"1641",
"1677",
"2149"... | [
"nonn"
] | 11 | 1 | 2 | [
"A125184",
"A260443",
"A391260",
"A391338",
"A391340"
] | null | Antti Karttunen, Dec 08 2025 | 2025-12-14T14:03:00 | oeisdata/seq/A391/A391340.seq | 38e2ca1e95ffb6751d32a96892efeb47 |
A391341 | Numbers k such that Stern polynomial B(5*k,x) is irreducible. | [
"1",
"5",
"11",
"13",
"19",
"23",
"25",
"29",
"35",
"37",
"41",
"43",
"47",
"49",
"53",
"59",
"61",
"67",
"79",
"83",
"85",
"89",
"95",
"97",
"101",
"103",
"109",
"115",
"125",
"131",
"133",
"139",
"151",
"157",
"161",
"163",
"173",
"175",
... | [
"nonn"
] | 19 | 1 | 2 | [
"A125184",
"A206284",
"A260443",
"A283991",
"A391341",
"A391342",
"A391345",
"A391347",
"A391349",
"A391350"
] | null | Antti Karttunen, Dec 12 2025 | 2025-12-13T17:44:18 | oeisdata/seq/A391/A391341.seq | 080b961b42a1f1529306f4364c1e17fa |
A391342 | Numbers k such that Stern polynomial B(5*k,x) is reducible. | [
"2",
"3",
"4",
"6",
"7",
"8",
"9",
"10",
"12",
"14",
"15",
"16",
"17",
"18",
"20",
"21",
"22",
"24",
"26",
"27",
"28",
"30",
"31",
"32",
"33",
"34",
"36",
"38",
"39",
"40",
"42",
"44",
"45",
"46",
"48",
"50",
"51",
"52",
"54",
"55",
"56... | [
"nonn"
] | 16 | 1 | 1 | [
"A008585",
"A125184",
"A206285",
"A260443",
"A283991",
"A391341",
"A391342",
"A391346",
"A391348",
"A391350"
] | null | Antti Karttunen, Dec 12 2025 | 2025-12-13T17:44:22 | oeisdata/seq/A391/A391342.seq | c2ace9542b280d7ff15b5e34912fad6a |
A391343 | Odd semiprimes k = p*q such that either k = A048720(A065621(p),x) or k = A048720(A065621(q),x) for some x. | [
"9",
"21",
"33",
"35",
"49",
"65",
"93",
"129",
"133",
"155",
"161",
"217",
"259",
"287",
"309",
"341",
"381",
"403",
"527",
"589",
"597",
"611",
"635",
"681",
"699",
"713",
"785",
"793",
"849",
"871",
"889",
"899",
"923",
"961",
"1047",
"1055",
... | [
"nonn"
] | 7 | 1 | 1 | [
"A046315",
"A048720",
"A065621",
"A391248",
"A391253",
"A391343",
"A391344"
] | null | Antti Karttunen, Dec 07 2025 | 2025-12-07T10:37:23 | oeisdata/seq/A391/A391343.seq | d8fb946e55f0d4da6f08a5656d1844e2 |
A391344 | Odd semiprimes k = p*q such that neither k = A048720(A065621(p),x) nor k = A048720(A065621(q),x) for any x. | [
"15",
"25",
"39",
"51",
"55",
"57",
"69",
"77",
"85",
"87",
"91",
"95",
"111",
"115",
"119",
"121",
"123",
"141",
"143",
"145",
"159",
"169",
"177",
"183",
"185",
"187",
"201",
"203",
"205",
"209",
"213",
"215",
"219",
"221",
"235",
"237",
"247... | [
"nonn"
] | 8 | 1 | 1 | [
"A046315",
"A048720",
"A065621",
"A391254",
"A391343",
"A391344"
] | null | Antti Karttunen, Dec 07 2025 | 2025-12-07T10:37:26 | oeisdata/seq/A391/A391344.seq | 78b2604c381413b060f16f621ca8268f |
A391345 | Numbers k that are multiples of 5 and for which Stern polynomial B(k,x) is irreducible. | [
"5",
"25",
"55",
"65",
"95",
"115",
"125",
"145",
"175",
"185",
"205",
"215",
"235",
"245",
"265",
"295",
"305",
"335",
"395",
"415",
"425",
"445",
"475",
"485",
"505",
"515",
"545",
"575",
"625",
"655",
"665",
"695",
"755",
"785",
"805",
"815",
... | [
"nonn"
] | 11 | 1 | 1 | [
"A008587",
"A125184",
"A186891",
"A260443",
"A391341",
"A391345"
] | null | Antti Karttunen, Dec 12 2025 | 2025-12-14T14:02:37 | oeisdata/seq/A391/A391345.seq | e3f4185723dce7dad53c62477915c760 |
A391346 | Numbers k such that Stern polynomial B(5*k,x) is a multiple of B(5,x). | [
"1",
"2",
"4",
"7",
"8",
"9",
"14",
"15",
"16",
"17",
"18",
"21",
"28",
"30",
"31",
"32",
"33",
"34",
"36",
"42",
"55",
"56",
"57",
"60",
"62",
"63",
"64",
"65",
"66",
"68",
"71",
"72",
"73",
"84",
"107",
"110",
"111",
"112",
"113",
"114"... | [
"nonn"
] | 16 | 1 | 2 | [
"A125184",
"A260443",
"A391342",
"A391346",
"A391347",
"A391348",
"A391566"
] | null | Antti Karttunen, Dec 13 2025 | 2025-12-15T01:49:17 | oeisdata/seq/A391/A391346.seq | 5bdb6c76c957a0242ce84551f83f0c98 |
A391347 | Numbers k such that Stern polynomial B(5*k,x) is not a multiple of B(5,x). | [
"3",
"5",
"6",
"10",
"11",
"12",
"13",
"19",
"20",
"22",
"23",
"24",
"25",
"26",
"27",
"29",
"35",
"37",
"38",
"39",
"40",
"41",
"43",
"44",
"45",
"46",
"47",
"48",
"49",
"50",
"51",
"52",
"53",
"54",
"58",
"59",
"61",
"67",
"69",
"70",
... | [
"nonn"
] | 8 | 1 | 1 | [
"A125184",
"A260443",
"A391341",
"A391346",
"A391347",
"A391349"
] | null | Antti Karttunen, Dec 13 2025 | 2025-12-13T17:44:31 | oeisdata/seq/A391/A391347.seq | 7390c5aaf594ed558838f53c8c8f0f3b |
A391348 | Numbers k such that Stern polynomial B(5*k,x) is equal to B(5,x)*B(k,x). | [
"1",
"2",
"4",
"7",
"8",
"9",
"14",
"16",
"18",
"28",
"32",
"36",
"55",
"56",
"57",
"64",
"71",
"72",
"73",
"110",
"112",
"114",
"128",
"142",
"144",
"146",
"220",
"224",
"228",
"256",
"277",
"284",
"288",
"292",
"335",
"439",
"440",
"441",
... | [
"nonn"
] | 16 | 1 | 2 | [
"A125184",
"A260443",
"A391260",
"A391338",
"A391342",
"A391346",
"A391348",
"A391349",
"A391350"
] | null | Antti Karttunen, Dec 13 2025 | 2025-12-13T17:44:46 | oeisdata/seq/A391/A391348.seq | b15403775747c520ccfed9ab636aad75 |
A391349 | Numbers k such that Stern polynomial B(5*k,x) is not equal to B(5,x)*B(k,x). | [
"3",
"5",
"6",
"10",
"11",
"12",
"13",
"15",
"17",
"19",
"20",
"21",
"22",
"23",
"24",
"25",
"26",
"27",
"29",
"30",
"31",
"33",
"34",
"35",
"37",
"38",
"39",
"40",
"41",
"42",
"43",
"44",
"45",
"46",
"47",
"48",
"49",
"50",
"51",
"52",
... | [
"nonn"
] | 14 | 1 | 1 | [
"A125184",
"A260443",
"A391260",
"A391339",
"A391341",
"A391347",
"A391348",
"A391349",
"A391350"
] | null | Antti Karttunen, Dec 13 2025 | 2025-12-13T17:44:42 | oeisdata/seq/A391/A391349.seq | e9869826685b0b3a5e704fa3b4f38c06 |
A391350 | Numbers k such that Stern polynomial B(5*k,x) is reducible, but not equal to B(5,x)*B(k,x). | [
"3",
"6",
"10",
"12",
"15",
"17",
"20",
"21",
"22",
"24",
"26",
"27",
"30",
"31",
"33",
"34",
"38",
"39",
"40",
"42",
"44",
"45",
"46",
"48",
"50",
"51",
"52",
"54",
"58",
"60",
"62",
"63",
"65",
"66",
"68",
"69",
"70",
"74",
"75",
"76",
... | [
"nonn"
] | 15 | 1 | 1 | [
"A125184",
"A260443",
"A391260",
"A391341",
"A391342",
"A391348",
"A391349",
"A391350"
] | null | Antti Karttunen, Dec 13 2025 | 2025-12-14T10:14:08 | oeisdata/seq/A391/A391350.seq | 326c505895a3360d5b9dbf0639e41fc4 |
A391351 | Numbers k such that 3*k - (greatest prime < 3*k) < (least prime > 3*k) - 3*k. | [
"1",
"8",
"11",
"16",
"18",
"21",
"25",
"28",
"30",
"38",
"39",
"44",
"47",
"51",
"53",
"56",
"58",
"61",
"67",
"68",
"71",
"72",
"78",
"81",
"84",
"86",
"88",
"91",
"95",
"98",
"99",
"106",
"107",
"111",
"113",
"118",
"120",
"123",
"125",
... | [
"nonn"
] | 10 | 1 | 2 | [
"A000027",
"A000040",
"A390788",
"A391351",
"A391352",
"A391353"
] | null | Clark Kimberling, Dec 10 2025 | 2025-12-27T15:51:15 | oeisdata/seq/A391/A391351.seq | d82521e9be48b19cb5cab46bae94af4a |
A391352 | Numbers k such that 3*k - (greatest prime < 3*k) = (least prime > 3*k) - 3*k. | [
"2",
"3",
"4",
"5",
"6",
"7",
"10",
"13",
"14",
"15",
"20",
"23",
"24",
"27",
"31",
"33",
"34",
"35",
"36",
"37",
"40",
"43",
"46",
"48",
"50",
"55",
"60",
"62",
"64",
"65",
"66",
"75",
"76",
"77",
"80",
"82",
"90",
"93",
"94",
"96",
"1... | [
"nonn"
] | 7 | 1 | 1 | [
"A000040",
"A391351",
"A391352",
"A391353"
] | null | Clark Kimberling, Dec 10 2025 | 2025-12-18T16:12:49 | oeisdata/seq/A391/A391352.seq | eddebed91d0ed793f12d61d7c9dd1595 |
A391353 | Numbers k such that 3*k - (greatest prime < 3*k) > (least prime > 3*k) - 3*k. | [
"9",
"12",
"17",
"19",
"22",
"26",
"29",
"32",
"41",
"42",
"45",
"49",
"52",
"54",
"57",
"59",
"63",
"69",
"70",
"73",
"74",
"79",
"83",
"85",
"87",
"89",
"92",
"97",
"101",
"102",
"109",
"110",
"112",
"115",
"119",
"122",
"124",
"126",
"12... | [
"nonn"
] | 5 | 1 | 1 | [
"A000027",
"A000040",
"A391351",
"A391352",
"A391353"
] | null | Clark Kimberling, Dec 10 2025 | 2025-12-17T14:13:20 | oeisdata/seq/A391/A391353.seq | 1d4e79379eadcdb5e8187fff582f44bb |
A391354 | Numbers k such that 4*k - (greatest prime < 4*k) < (least prime > 4*k) - 4*k. | [
"2",
"5",
"6",
"8",
"11",
"12",
"17",
"20",
"21",
"23",
"26",
"29",
"32",
"33",
"35",
"38",
"41",
"42",
"46",
"50",
"51",
"53",
"54",
"56",
"61",
"63",
"66",
"68",
"71",
"74",
"77",
"80",
"83",
"85",
"90",
"92",
"95",
"96",
"98",
"101",
... | [
"nonn"
] | 7 | 1 | 1 | [
"A000027",
"A000040",
"A390788",
"A391354",
"A391355",
"A391356"
] | null | Clark Kimberling, Dec 14 2025 | 2025-12-27T16:02:51 | oeisdata/seq/A391/A391354.seq | 1cf563166323db83ccaaba3e01b5a7b8 |
A391355 | Numbers k such that 4*k - (greatest prime < 4*k) = (least prime > 4*k) - 4*k. | [
"1",
"3",
"14",
"15",
"16",
"18",
"19",
"27",
"30",
"36",
"40",
"44",
"45",
"48",
"57",
"59",
"60",
"65",
"72",
"75",
"78",
"81",
"87",
"89",
"94",
"105",
"108",
"109",
"133",
"136",
"138",
"140",
"149",
"150",
"151",
"159",
"164",
"165",
"... | [
"nonn"
] | 6 | 1 | 2 | [
"A000027",
"A000040",
"A391351",
"A391354",
"A391355",
"A391356"
] | null | Clark Kimberling, Dec 14 2025 | 2025-12-28T16:05:55 | oeisdata/seq/A391/A391355.seq | 659115fd79795c843781713fd8537306 |
A391356 | Numbers k such that 4*k - (greatest prime < 4*k) > (least prime > 4*k) - 4*k. | [
"4",
"7",
"9",
"10",
"13",
"22",
"24",
"25",
"28",
"31",
"34",
"37",
"39",
"43",
"47",
"49",
"52",
"55",
"58",
"62",
"64",
"67",
"69",
"70",
"73",
"76",
"79",
"82",
"84",
"86",
"88",
"91",
"93",
"97",
"99",
"100",
"102",
"104",
"107",
"11... | [
"nonn"
] | 5 | 1 | 1 | [
"A000027",
"A000040",
"A391351",
"A391354",
"A391355",
"A391356"
] | null | Clark Kimberling, Dec 18 2025 | 2025-12-20T13:29:04 | oeisdata/seq/A391/A391356.seq | 33618893e70e2616e62b3942f78abc97 |
A391357 | Rectangular array R read by falling antidiagonals: R(n,k) = prime(n) + prime(n+k). | [
"5",
"7",
"8",
"9",
"10",
"12",
"13",
"14",
"16",
"18",
"15",
"16",
"18",
"20",
"24",
"19",
"20",
"22",
"24",
"28",
"30",
"21",
"22",
"24",
"26",
"30",
"32",
"36",
"25",
"26",
"28",
"30",
"34",
"36",
"40",
"42",
"31",
"32",
"34",
"36",
... | [
"nonn",
"tabl",
"easy"
] | 7 | 1 | 1 | [
"A001043",
"A048448",
"A052147",
"A092390",
"A113935",
"A175222",
"A175223",
"A391357",
"A391358",
"A391359"
] | null | Clark Kimberling, Dec 18 2025 | 2025-12-23T00:11:09 | oeisdata/seq/A391/A391357.seq | 8d6a830b37ed3933edc61d3f1d9980dc |
A391358 | Rectangular array R read by falling antidiagonals: R(n,k) = prime(k) + prime(n+k). | [
"5",
"8",
"7",
"12",
"10",
"9",
"18",
"16",
"14",
"13",
"24",
"20",
"18",
"16",
"15",
"30",
"28",
"24",
"22",
"20",
"19",
"36",
"32",
"30",
"26",
"24",
"22",
"21",
"42",
"40",
"36",
"34",
"30",
"28",
"26",
"25",
"52",
"48",
"46",
"42",
... | [
"nonn",
"tabl",
"easy"
] | 7 | 1 | 1 | [
"A391357",
"A391358",
"A391359"
] | null | Clark Kimberling, Dec 18 2025 | 2025-12-23T00:10:58 | oeisdata/seq/A391/A391358.seq | e8bb54160ec42229c622719cfa92a64d |
A391359 | Rectangular array R read by falling antidiagonals: R(n,k) = (prime(n) + prime(n+k))/2, for n>=2, k>=1. | [
"4",
"5",
"6",
"7",
"8",
"9",
"8",
"9",
"10",
"12",
"10",
"11",
"12",
"14",
"15",
"11",
"12",
"13",
"15",
"16",
"18",
"13",
"14",
"15",
"17",
"18",
"20",
"21",
"16",
"17",
"18",
"20",
"21",
"23",
"24",
"26",
"17",
"18",
"19",
"21",
"22"... | [
"nonn",
"tabl",
"easy"
] | 7 | 1 | 1 | [
"A065305",
"A391357",
"A391358",
"A391359"
] | null | Clark Kimberling, Dec 20 2025 | 2025-12-23T00:11:04 | oeisdata/seq/A391/A391359.seq | ef4c6716607acb14bfebecfffaa0880e |
A391360 | Number of irreducible elements of Z[(1+sqrt(-15))/2] (the ring of integers of Q(sqrt(-15))) of norm n up to association. | [
"0",
"0",
"0",
"3",
"0",
"2",
"0",
"0",
"1",
"2",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"2",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"2",
"0",
"0",
"4",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"... | [
"nonn",
"easy"
] | 19 | 1 | 4 | [
"A033212",
"A091731",
"A106859",
"A191018",
"A191062",
"A341786",
"A390422",
"A391360",
"A391361",
"A391362",
"A391363"
] | null | Jianing Song, Dec 07 2025 | 2025-12-27T19:24:50 | oeisdata/seq/A391/A391360.seq | ec2cba1a52d532945f8b355a4fb88f6d |
A391361 | Number of irreducible elements of Z[sqrt(-6)] of norm n up to association. | [
"0",
"0",
"0",
"1",
"0",
"1",
"2",
"0",
"1",
"2",
"0",
"0",
"0",
"0",
"2",
"0",
"0",
"0",
"0",
"0",
"0",
"2",
"0",
"0",
"3",
"0",
"0",
"0",
"0",
"0",
"2",
"0",
"2",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"... | [
"nonn",
"easy"
] | 18 | 1 | 7 | [
"A033199",
"A084865",
"A091731",
"A157437",
"A191059",
"A390498",
"A391360",
"A391361",
"A391362",
"A391364",
"A391366"
] | null | Jianing Song, Dec 07 2025 | 2025-12-27T16:02:22 | oeisdata/seq/A391/A391361.seq | 078a7c28e353741e8b03076b1d2a038d |
A391362 | Number of irreducible elements of Z[sqrt(10)] of norm n up to association. | [
"0",
"0",
"0",
"1",
"0",
"2",
"0",
"0",
"3",
"1",
"0",
"0",
"0",
"0",
"2",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"2",
"0",
"0",
"0",
"0",
"2",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"4",
"0",
"2",
"0",
"0",
"0",
"0",
"... | [
"nonn",
"easy"
] | 16 | 1 | 6 | [
"A038880",
"A091731",
"A097955",
"A141179",
"A141180",
"A262362",
"A390526",
"A391360",
"A391361",
"A391362",
"A391367"
] | null | Jianing Song, Dec 07 2025 | 2025-12-27T16:13:51 | oeisdata/seq/A391/A391362.seq | f86d13231bf393993a31c261f61d2adf |
A391363 | Numbers with more than one factorization (up to association) in Z[(1+sqrt(-15))/2], the ring of integers of Q(sqrt(-15)). | [
"4",
"6",
"8",
"10",
"12",
"15",
"16",
"18",
"20",
"24",
"28",
"30",
"32",
"34",
"36",
"40",
"42",
"44",
"45",
"46",
"48",
"50",
"51",
"52",
"54",
"56",
"60",
"64",
"66",
"68",
"69",
"70",
"72",
"75",
"76",
"78",
"80",
"84",
"85",
"88",
... | [
"nonn"
] | 21 | 1 | 1 | [
"A033212",
"A106859",
"A191018",
"A191062",
"A262362",
"A262828",
"A341786",
"A390422",
"A391360",
"A391363",
"A391364"
] | null | Jianing Song, Dec 07 2025 | 2025-12-27T16:02:35 | oeisdata/seq/A391/A391363.seq | 40a15a2d34f30466eb80ba58bd320270 |
A391364 | Numbers with more than one factorization (up to association) in Z[sqrt(-6)]. | [
"6",
"10",
"12",
"15",
"18",
"20",
"22",
"24",
"25",
"30",
"33",
"36",
"40",
"42",
"44",
"45",
"48",
"50",
"54",
"55",
"58",
"60",
"66",
"70",
"72",
"75",
"78",
"80",
"84",
"87",
"88",
"90",
"96",
"99",
"100",
"102",
"105",
"106",
"108",
... | [
"nonn",
"easy"
] | 21 | 1 | 1 | [
"A033199",
"A084865",
"A157437",
"A191059",
"A262362",
"A262828",
"A390498",
"A391361",
"A391363",
"A391364",
"A391366"
] | null | Jianing Song, Dec 07 2025 | 2025-12-27T16:03:00 | oeisdata/seq/A391/A391364.seq | e6d25f9c64e12553b8c175b930bd81d6 |
A391366 | Norms of prime ideals of Z[sqrt(-6)]. | [
"2",
"3",
"5",
"7",
"11",
"29",
"31",
"53",
"59",
"73",
"79",
"83",
"97",
"101",
"103",
"107",
"127",
"131",
"149",
"151",
"169",
"173",
"179",
"193",
"197",
"199",
"223",
"227",
"241",
"251",
"269",
"271",
"289",
"293",
"313",
"317",
"337",
... | [
"nonn",
"easy"
] | 21 | 1 | 1 | [
"A033199",
"A055025",
"A055664",
"A055673",
"A084865",
"A090348",
"A091727",
"A109017",
"A157437",
"A191059",
"A192013",
"A296924",
"A341783",
"A341784",
"A341785",
"A341786",
"A341787",
"A341788",
"A341789",
"A341790",
"A391366",
"A391367",
"A391369",
"A391370",
"A39... | null | Jianing Song, Dec 07 2025 | 2025-12-11T12:26:37 | oeisdata/seq/A391/A391366.seq | 6e735070d16b1b1daf32972e99453048 |
A391367 | Norms of prime ideals of Z[sqrt(10)]. | [
"2",
"3",
"5",
"13",
"31",
"37",
"41",
"43",
"49",
"53",
"67",
"71",
"79",
"83",
"89",
"107",
"121",
"151",
"157",
"163",
"173",
"191",
"197",
"199",
"227",
"239",
"241",
"271",
"277",
"281",
"283",
"289",
"293",
"307",
"311",
"317",
"347",
"... | [
"nonn",
"easy"
] | 16 | 1 | 1 | [
"A035192",
"A038879",
"A038880",
"A055025",
"A055664",
"A055673",
"A090348",
"A091727",
"A097955",
"A141179",
"A141180",
"A341783",
"A341784",
"A341785",
"A341786",
"A341787",
"A341788",
"A341789",
"A341790",
"A391366",
"A391367",
"A391369",
"A391370",
"A391371",
"A39... | null | Jianing Song, Dec 07 2025 | 2025-12-12T15:08:41 | oeisdata/seq/A391/A391367.seq | d230d5ed046bee9315611e8028966479 |
A391368 | Number of positive integers k with an arithmetic mean of divisors equal to n. | [
"1",
"1",
"2",
"1",
"0",
"3",
"2",
"1",
"3",
"2",
"0",
"4",
"1",
"3",
"4",
"1",
"0",
"5",
"2",
"1",
"5",
"1",
"0",
"5",
"0",
"2",
"4",
"4",
"0",
"6",
"2",
"1",
"1",
"1",
"1",
"8",
"1",
"2",
"3",
"3",
"0",
"8",
"0",
"1",
"9",
"... | [
"nonn"
] | 9 | 1 | 3 | [
"A000005",
"A000203",
"A157846",
"A157847",
"A162538",
"A391368"
] | null | Joe Anderson, Dec 07 2025 | 2025-12-14T13:55:51 | oeisdata/seq/A391/A391368.seq | c0c885be48b378da6cecea4af75961f2 |
A391369 | Absolute values of norms of prime elements in Z[sqrt(3)]. | [
"2",
"3",
"11",
"13",
"23",
"25",
"37",
"47",
"49",
"59",
"61",
"71",
"73",
"83",
"97",
"107",
"109",
"131",
"157",
"167",
"179",
"181",
"191",
"193",
"227",
"229",
"239",
"241",
"251",
"263",
"277",
"289",
"311",
"313",
"337",
"347",
"349",
... | [
"nonn"
] | 17 | 1 | 1 | [
"A003630",
"A035194",
"A038874",
"A055025",
"A055664",
"A055673",
"A090348",
"A091727",
"A097933",
"A110161",
"A341783",
"A341784",
"A341785",
"A341786",
"A341787",
"A341788",
"A341789",
"A341790",
"A391366",
"A391367",
"A391369",
"A391370",
"A391371"
] | null | Jianing Song, Dec 07 2025 | 2025-12-12T15:08:38 | oeisdata/seq/A391/A391369.seq | 851e7e1f9978d882a4c3275a3574f52f |
A391370 | Absolute values of norms of prime elements in Z[(1+sqrt(21))/2], the ring of integers of Q(sqrt(21)). | [
"3",
"4",
"5",
"7",
"17",
"37",
"41",
"43",
"47",
"59",
"67",
"79",
"83",
"89",
"101",
"109",
"121",
"127",
"131",
"151",
"163",
"167",
"169",
"173",
"193",
"211",
"227",
"251",
"257",
"269",
"277",
"293",
"311",
"331",
"337",
"353",
"361",
"... | [
"nonn"
] | 15 | 1 | 1 | [
"A035203",
"A038893",
"A038894",
"A055025",
"A055664",
"A055673",
"A090348",
"A091727",
"A322829",
"A341783",
"A341784",
"A341785",
"A341786",
"A341787",
"A341788",
"A341789",
"A341790",
"A391366",
"A391367",
"A391369",
"A391370",
"A391371"
] | null | Jianing Song, Dec 07 2025 | 2025-12-12T15:06:45 | oeisdata/seq/A391/A391370.seq | ed418045f8202b77e7b718c2180df2a1 |
A391371 | Absolute values of norms of prime elements in Z[sqrt(6)]. | [
"2",
"3",
"5",
"19",
"23",
"29",
"43",
"47",
"49",
"53",
"67",
"71",
"73",
"97",
"101",
"121",
"139",
"149",
"163",
"167",
"169",
"173",
"191",
"193",
"197",
"211",
"239",
"241",
"263",
"269",
"283",
"289",
"293",
"307",
"311",
"313",
"317",
... | [
"nonn"
] | 16 | 1 | 1 | [
"A035188",
"A038876",
"A038877",
"A055025",
"A055664",
"A055673",
"A090348",
"A091727",
"A097934",
"A322796",
"A341783",
"A341784",
"A341785",
"A341786",
"A341787",
"A341788",
"A341789",
"A341790",
"A391366",
"A391367",
"A391369",
"A391370",
"A391371"
] | null | Jianing Song, Dec 07 2025 | 2025-12-12T15:08:34 | oeisdata/seq/A391/A391371.seq | 3ca51e3f167d61f455ec01e4ab754a0e |
A391372 | a(n) = 2*a(n-1)^2 + a(n-1) + 1 with a(0) = 0. | [
"0",
"1",
"4",
"37",
"2776",
"15415129",
"475252419588412",
"451729724649280503419388951901",
"408119488263429563276016854205074047944119811268657971979504"
] | [
"nonn"
] | 26 | 0 | 3 | [
"A010685",
"A010888",
"A084849",
"A391372"
] | null | Timothy L. Tiffin, Dec 07 2025 | 2025-12-21T15:05:23 | oeisdata/seq/A391/A391372.seq | 82e6a0d310194304e2859570e78aaac4 |
A391373 | The largest number with an arithmetic mean of divisors equal to n or 0 is there is no such number. | [
"1",
"3",
"6",
"7",
"0",
"15",
"20",
"21",
"30",
"27",
"0",
"42",
"45",
"60",
"56",
"31",
"0",
"70",
"49",
"57",
"96",
"43",
"0",
"105",
"0",
"126",
"110",
"140",
"0",
"168",
"150",
"93",
"86",
"67",
"116",
"210",
"73",
"147",
"198",
"189... | [
"nonn"
] | 11 | 1 | 2 | [
"A000005",
"A000203",
"A003601",
"A157847",
"A162538",
"A391373"
] | null | Joe Anderson, Dec 07 2025 | 2025-12-14T16:25:09 | oeisdata/seq/A391/A391373.seq | 0acbd4adcd46a03aaa9c1fd412c01099 |
A391374 | Number of positive integers k such that k's arithmetic mean of divisors is at most n. | [
"1",
"3",
"6",
"8",
"11",
"14",
"18",
"20",
"23",
"26",
"30",
"35",
"37",
"41",
"45",
"47",
"49",
"55",
"60",
"62",
"68",
"69",
"72",
"79",
"82",
"84",
"90",
"94",
"96",
"102",
"106",
"111",
"113",
"115",
"116",
"124",
"127",
"134",
"138",
... | [
"nonn"
] | 6 | 1 | 2 | [
"A000005",
"A000203",
"A391368",
"A391374"
] | null | Joe Anderson, Dec 07 2025 | 2025-12-14T14:18:13 | oeisdata/seq/A391/A391374.seq | e3ee7c9333c980e152580a71836a8630 |
A391375 | Powers k^m, m > 1, where k is an odd Achilles number. | [
"455625",
"1265625",
"1750329",
"9529569",
"10673289",
"20820969",
"36905625",
"37515625",
"60886809",
"73530625",
"95004009",
"102515625",
"141776649",
"143496441",
"204004089",
"228765625",
"284765625",
"307546875",
"390971529",
"446265625",
"515607849",
"673246809",
"7... | [
"nonn",
"easy"
] | 5 | 1 | 1 | [
"A001597",
"A001694",
"A005408",
"A052486",
"A126706",
"A131605",
"A286708",
"A383394",
"A390953",
"A391375",
"A391376"
] | null | Michael De Vlieger, Dec 09 2025 | 2025-12-17T14:42:14 | oeisdata/seq/A391/A391375.seq | 201635e4da88f7f8ed06e8fed5c0d770 |
A391376 | Powers k^m, m > 1, where k is an even Achilles number. | [
"5184",
"11664",
"40000",
"82944",
"153664",
"186624",
"250000",
"373248",
"419904",
"640000",
"746496",
"937024",
"944784",
"1259712",
"1327104",
"1827904",
"1882384",
"2458624",
"3240000",
"3779136",
"4000000",
"5345344",
"6718464",
"7290000",
"8000000",
"8340544"... | [
"nonn",
"easy"
] | 5 | 1 | 1 | [
"A001597",
"A001694",
"A005843",
"A052486",
"A126706",
"A131605",
"A286708",
"A383394",
"A390952",
"A391375",
"A391376"
] | null | Michael De Vlieger, Dec 09 2025 | 2025-12-17T14:41:01 | oeisdata/seq/A391/A391376.seq | 502d72f206a439dcbdce20c2b7a20ae3 |
A391378 | Expansion of g^2/(1 + x*g), where g = 1+x*g^4 is the g.f. of A002293. | [
"1",
"1",
"7",
"40",
"267",
"1897",
"14123",
"108719",
"858421",
"6913914",
"56583401",
"469200322",
"3933669482",
"33287843079",
"283956543780",
"2439153154289",
"21080183230758",
"183168147509467",
"1599221574473345",
"14022758576502463",
"123435372854088656",
"1090356552... | [
"nonn"
] | 7 | 0 | 3 | [
"A002293",
"A387982",
"A391378"
] | null | Seiichi Manyama, Dec 07 2025 | 2025-12-08T04:29:46 | oeisdata/seq/A391/A391378.seq | 0f32e04f6df020554384afbbc111d824 |
A391379 | Expansion of g^2/(1 + x*g^2), where g = 1+x*g^4 is the g.f. of A002293. | [
"1",
"1",
"6",
"35",
"232",
"1646",
"12239",
"94137",
"742825",
"5980056",
"48922556",
"405553786",
"3399234751",
"28759383055",
"245284421794",
"2106648344723",
"18204169010624",
"158160107826385",
"1380740162723725",
"12105923730466112",
"106553900171498799",
"94116760517... | [
"nonn"
] | 10 | 0 | 3 | [
"A002293",
"A390740",
"A391379"
] | null | Seiichi Manyama, Dec 07 2025 | 2025-12-08T04:30:51 | oeisdata/seq/A391/A391379.seq | df7e2f6a3234894834ade2b45b657d0c |
A391380 | Expansion of g*(1 + x*g), where g = 1+x*g^3 is the g.f. of A001764. | [
"1",
"2",
"5",
"19",
"85",
"416",
"2156",
"11628",
"64581",
"366850",
"2121405",
"12446655",
"73908588",
"443329264",
"2682282440",
"16350019688",
"100312427493",
"618978133158",
"3838830395855",
"23916064782225",
"149605584539565",
"939295627587240",
"5917060156672560",
... | [
"nonn",
"easy"
] | 13 | 0 | 2 | [
"A001764",
"A101409",
"A167422",
"A390519",
"A391380",
"A391381",
"A391382"
] | null | Seiichi Manyama, Dec 08 2025 | 2025-12-08T04:32:07 | oeisdata/seq/A391/A391380.seq | 3c165de343627378ba8329c2340b30af |
A391381 | Expansion of g*(1 + x*g^2), where g = 1+x*g^4 is the g.f. of A002293. | [
"1",
"2",
"7",
"37",
"231",
"1581",
"11473",
"86710",
"675207",
"5379616",
"43645052",
"359336341",
"2994665297",
"25213773690",
"214149202470",
"1832589292380",
"15785734361415",
"136764083705832",
"1190973643069588",
"10418763855670244",
"91519130263741180",
"806893777849... | [
"nonn",
"easy"
] | 12 | 0 | 2 | [
"A002293",
"A167422",
"A390710",
"A391380",
"A391381",
"A391382"
] | null | Seiichi Manyama, Dec 08 2025 | 2025-12-08T04:33:02 | oeisdata/seq/A391/A391381.seq | fa7080203e7ec4b4864c40dec92dd488 |
A391382 | Expansion of g*(1 + x*g^3), where g = 1+x*g^5 is the g.f. of A002294. | [
"1",
"2",
"9",
"61",
"489",
"4301",
"40131",
"390104",
"3907977",
"40062412",
"418254034",
"4431613550",
"47532700995",
"515094994701",
"5631040056392",
"62026042961616",
"687736507905865",
"7669858226447790",
"85977241224449355",
"968212072361926899",
"10948257397698469394",... | [
"nonn",
"easy"
] | 10 | 0 | 2 | [
"A002294",
"A167422",
"A391380",
"A391381",
"A391382"
] | null | Seiichi Manyama, Dec 08 2025 | 2025-12-08T04:34:03 | oeisdata/seq/A391/A391382.seq | c6289c2fa89282b706219f4f03542721 |
A391383 | Expansion of g/(1 - x*g^6), where g = 1+x*g^5 is the g.f. of A002294. | [
"1",
"2",
"13",
"105",
"938",
"8893",
"87723",
"890325",
"9232805",
"97376126",
"1041089019",
"11256502919",
"122861952973",
"1351837036390",
"14977717978726",
"166953700523302",
"1870943152825162",
"21065820665414499",
"238193982444276850",
"2703539335002781050",
"3079115293... | [
"nonn"
] | 12 | 0 | 2 | [
"A002294",
"A026726",
"A390519",
"A390710",
"A391382",
"A391383"
] | null | Seiichi Manyama, Dec 08 2025 | 2025-12-08T04:35:41 | oeisdata/seq/A391/A391383.seq | 47eab128e7329735fc3fe2d9214e3a8a |
A391385 | a(n) is the smallest number k > 1 such that k^(2^m) + 1 is prime for all m = 1 to n, but not for m=n+1. | [
"10",
"6",
"4",
"2",
"2090676"
] | [
"nonn",
"more"
] | 6 | 1 | 1 | [
"A389254",
"A391385"
] | null | Michel Marcus, Dec 08 2025 | 2025-12-08T08:57:27 | oeisdata/seq/A391/A391385.seq | 61e6cbe94328231772c6dd88f3d8ab95 |
A391386 | Irregular triangle read by rows: powers of 2 in the factorization of A391261; 0 if A391261(n,k) = 0. | [
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"2",
"1",
"0",
"2",
"0",
"0",
"3",
"2",
"2",
"0",
"3",
"0",
"3",
"0",
"0",
"3",
"0",
"1",
"0",
"4",
"0",
"2",
"0",
"0",
"5",
"4",
"5",
"2",
"1",
"0",
"4",
"0",
"4",
"0",
"0",
"6",
"5",
"... | [
"nonn",
"tabf"
] | 22 | 1 | 9 | [
"A055034",
"A389480",
"A391261",
"A391386",
"A391387"
] | null | A.H.M. Smeets, Dec 08 2025 | 2025-12-16T13:44:10 | oeisdata/seq/A391/A391386.seq | 7426c77b6bd8a95f624d67810f7e0258 |
A391387 | Irregular triangle read by rows: greatest odd divisor of A391261(n,k), signed; 0 if A391261(n,k) = 0. | [
"1",
"1",
"0",
"1",
"-1",
"1",
"0",
"-1",
"1",
"-1",
"-1",
"1",
"0",
"-3",
"1",
"-1",
"-1",
"1",
"1",
"0",
"-1",
"0",
"1",
"1",
"0",
"-3",
"-1",
"1",
"0",
"-5",
"0",
"5",
"1",
"-1",
"-1",
"3",
"3",
"-1",
"1",
"0",
"-1",
"0",
"1",
... | [
"sign",
"tabf"
] | 16 | 1 | 14 | [
"A000265",
"A055034",
"A389480",
"A391261",
"A391386",
"A391387"
] | null | A.H.M. Smeets, Dec 08 2025 | 2025-12-16T13:37:49 | oeisdata/seq/A391/A391387.seq | 39487130ab70448e6fd6de26c8918a16 |
A391388 | Site percolation series for square lattice: coefficients of the power series expansion in powers of q=1-p of the probability that a given site (not assumed to be open) belongs to the infinite cluster, where p is the probability that a site is open. | [
"1",
"-1",
"0",
"0",
"-1",
"1",
"-4",
"-4",
"-15",
"-5",
"-158",
"234",
"-1349",
"2713",
"-13704",
"42676",
"-172825",
"559053",
"-2029776",
"6774936",
"-23900386",
"81129962",
"-282099620",
"963894132",
"-3331512669",
"11422580633",
"-39350336472",
"13493982108... | [
"sign"
] | 10 | 0 | 7 | [
"A338210",
"A391388",
"A391389",
"A391390",
"A391392"
] | null | Pontus von Brömssen, Dec 10 2025 | 2025-12-18T07:59:04 | oeisdata/seq/A391/A391388.seq | b2dc0fa71d8be201c96c1956df64eaad |
A391389 | Site percolation series for square lattice: coefficients of the power series expansion in powers of q=1-p of the probability that a given open site belongs to the infinite cluster, where p is the probability that a site is open. | [
"1",
"0",
"0",
"0",
"-1",
"0",
"-4",
"-8",
"-23",
"-28",
"-186",
"48",
"-1301",
"1412",
"-12292",
"30384",
"-142441",
"416612",
"-1613164",
"5161772",
"-18738614",
"62391348",
"-219708272",
"744185860",
"-2587326809",
"8835253824",
"-30515082648",
"104424738432"... | [
"sign"
] | 11 | 0 | 7 | [
"A338210",
"A391388",
"A391389",
"A391391",
"A391393"
] | null | Pontus von Brömssen, Dec 10 2025 | 2025-12-18T07:59:08 | oeisdata/seq/A391/A391389.seq | 9666794962293e45ac67c863402d1be9 |
A391390 | Site percolation series for triangular lattice: coefficients of the power series expansion in powers of q=1-p of the probability that a given site (not assumed to be open) belongs to the infinite cluster, where p is the probability that a site is open. | [
"1",
"-1",
"0",
"0",
"0",
"0",
"-1",
"1",
"-6",
"6",
"-27",
"33",
"-117",
"183",
"-606",
"1172",
"-3506",
"7872",
"-22412",
"53570",
"-142197",
"339225",
"-859629"
] | [
"sign",
"more"
] | 6 | 0 | 9 | [
"A391388",
"A391390",
"A391391",
"A391392"
] | null | Pontus von Brömssen, Dec 10 2025 | 2025-12-12T10:56:23 | oeisdata/seq/A391/A391390.seq | ea1b58e14a4ca0cec7e9148d30d2e215 |
A391391 | Site percolation series for triangular lattice: coefficients of the power series expansion in powers of q=1-p of the probability that a given open site belongs to the infinite cluster, where p is the probability that a site is open. | [
"1",
"0",
"0",
"0",
"0",
"0",
"-1",
"0",
"-6",
"0",
"-27",
"6",
"-111",
"72",
"-534",
"638",
"-2868",
"5004",
"-17408",
"36162",
"-106035",
"233190",
"-626439"
] | [
"sign",
"more"
] | 6 | 0 | 9 | [
"A391389",
"A391390",
"A391391",
"A391393"
] | null | Pontus von Brömssen, Dec 10 2025 | 2025-12-12T10:56:11 | oeisdata/seq/A391/A391391.seq | 0acd8a99c4e30423c82c78d2d01f3a72 |
A391392 | Site percolation series for hexagonal lattice: coefficients of the power series expansion in powers of q=1-p of the probability that a given site (not assumed to be open) belongs to the infinite cluster, where p is the probability that a site is open. | [
"1",
"-1",
"0",
"-1",
"-2",
"-3",
"-22",
"-8",
"-324",
"157",
"-4159",
"8988",
"-58973",
"159656"
] | [
"sign",
"more"
] | 5 | 0 | 5 | [
"A391388",
"A391390",
"A391392",
"A391393"
] | null | Pontus von Brömssen, Dec 10 2025 | 2025-12-12T10:56:02 | oeisdata/seq/A391/A391392.seq | 00b753658145f127825ca25a47880e22 |
A391393 | Site percolation series for hexagonal lattice: coefficients of the power series expansion in powers of q=1-p of the probability that a given open site belongs to the infinite cluster, where p is the probability that a site is open. | [
"1",
"0",
"0",
"-1",
"-3",
"-6",
"-28",
"-36",
"-360",
"-203",
"-4362",
"4626",
"-54347",
"105309"
] | [
"sign",
"more"
] | 5 | 0 | 5 | [
"A391389",
"A391391",
"A391392",
"A391393"
] | null | Pontus von Brömssen, Dec 10 2025 | 2025-12-12T10:55:52 | oeisdata/seq/A391/A391393.seq | 4d00966af16b52299413e98c06e3c461 |
A391396 | Numbers k such that k and k+1 are both numbers whose number of divisors is 3 times a power of 2 (A377562). | [
"44",
"49",
"75",
"98",
"116",
"147",
"171",
"242",
"243",
"244",
"260",
"275",
"315",
"332",
"360",
"363",
"387",
"475",
"476",
"507",
"524",
"531",
"539",
"548",
"549",
"603",
"604",
"636",
"692",
"724",
"725",
"735",
"747",
"764",
"774",
"819"... | [
"nonn",
"easy"
] | 11 | 1 | 1 | [
"A372690",
"A377562",
"A388069",
"A391396",
"A391397"
] | null | Amiram Eldar, Dec 08 2025 | 2025-12-14T01:50:17 | oeisdata/seq/A391/A391396.seq | ba33e0c62a0f5d78c2ae51378131d15e |
A391397 | Numbers k such that d(k+1)/d(k) = 2^m for some integer m (positive, zero, or negative), where d(k) is the number of divisors of k. | [
"1",
"2",
"5",
"6",
"7",
"10",
"13",
"14",
"21",
"22",
"23",
"26",
"29",
"30",
"33",
"34",
"37",
"38",
"39",
"40",
"41",
"42",
"44",
"46",
"49",
"53",
"54",
"55",
"56",
"57",
"58",
"61",
"65",
"66",
"69",
"70",
"73",
"75",
"77",
"78",
"... | [
"nonn",
"easy"
] | 23 | 1 | 2 | [
"A000005",
"A036537",
"A372690",
"A377562",
"A391396",
"A391397"
] | null | Amiram Eldar, Dec 08 2025 | 2025-12-14T02:33:21 | oeisdata/seq/A391/A391397.seq | 02373f0c6544f07917507f93f928ebd4 |
A391398 | Number of compositions of n where the median of parts equals 1. | [
"1",
"1",
"3",
"6",
"10",
"21",
"43",
"81",
"161",
"325",
"637",
"1260",
"2520",
"4999",
"9917",
"19770",
"39354",
"78275",
"155969",
"310818",
"619174",
"1234199",
"2460905",
"4906597",
"9785125",
"19518887",
"38937907",
"77686076",
"155017552",
"309355889"... | [
"nonn"
] | 24 | 1 | 3 | [
"A008683",
"A011782",
"A388070",
"A391398"
] | null | Austen M. Fletcher, Dec 08 2025 | 2025-12-10T18:17:02 | oeisdata/seq/A391/A391398.seq | c99ccf743ab541b078faa930f3cfeaab |
A391399 | a(n) = Sum_{k=0..floor(n/3)} binomial(k,2*n-6*k). | [
"1",
"0",
"0",
"1",
"0",
"0",
"1",
"1",
"0",
"1",
"3",
"0",
"1",
"6",
"1",
"1",
"10",
"5",
"1",
"15",
"15",
"2",
"21",
"35",
"8",
"28",
"70",
"29",
"37",
"126",
"85",
"54",
"210",
"211",
"100",
"331",
"463",
"231",
"506",
"925",
"573",
... | [
"nonn",
"new"
] | 16 | 0 | 11 | [
"A005251",
"A062200",
"A391265",
"A391399",
"A392250"
] | null | Seiichi Manyama, Jan 05 2026 | 2026-01-06T04:06:17 | oeisdata/seq/A391/A391399.seq | 8efb508352f2e2b663a6eb7801e53e1d |
A391400 | Decimal expansion of the real solution of 2*sqrt(1-h^2) - Pi*h + 2*h*arcsin(h) = 1. | [
"3",
"6",
"0",
"0",
"3",
"4",
"9",
"8",
"2",
"8",
"0",
"8",
"7",
"0",
"9",
"6",
"5",
"4",
"0",
"7",
"9",
"6",
"5",
"0",
"5",
"0",
"6",
"7",
"3",
"7",
"0",
"0",
"7",
"4",
"8",
"9",
"8",
"8",
"7",
"7",
"9",
"6",
"7",
"8",
"4",
"... | [
"nonn",
"cons"
] | 18 | 0 | 1 | [
"A086751",
"A390401",
"A391400"
] | null | Stefano Spezia, Dec 08 2025 | 2025-12-13T23:17:48 | oeisdata/seq/A391/A391400.seq | c3588184a87dbf706feeea209bdda99a |
A391401 | Primes obtained by iterating the map prime(j) -> prime(j + prime(j) + 1) starting at 2. | [
"2",
"7",
"37",
"229",
"1811",
"18253",
"228959",
"3487189",
"63129359",
"1334379911",
"32446334281",
"896300577883",
"27831162033881",
"962606024675719",
"36795183927085811",
"1543768264352117803",
"70665478851360297731",
"3510376002304544358389",
"188348462136537160887367"
] | [
"nonn",
"more"
] | 38 | 1 | 1 | [
"A000040",
"A093502",
"A391401",
"A391616"
] | null | Bruce Nye, Dec 08 2025 | 2025-12-25T09:41:35 | oeisdata/seq/A391/A391401.seq | cb8c9184cecfaae8951da09cbe77feb8 |
A391402 | Triangle read by rows: T(n,k) is k-th entry of the toric g-vector of the n-dimensional cyclohedron, 0 <= k <= floor(n/2). | [
"1",
"1",
"1",
"3",
"1",
"16",
"1",
"65",
"20",
"1",
"246",
"225",
"1",
"917",
"1659",
"175",
"1",
"3424",
"10192",
"3136",
"1",
"12861",
"56664",
"34104",
"1764",
"1",
"48610",
"296055",
"291600",
"44100",
"1",
"184745",
"1482965",
"2157705",
"639... | [
"nonn",
"tabf"
] | 28 | 0 | 4 | [
"A000891",
"A337900",
"A381676",
"A391402",
"A391403"
] | null | Richard Ehrenborg, Dec 08 2025 | 2025-12-28T18:47:18 | oeisdata/seq/A391/A391402.seq | ff2464b2956a0333b56e802ef82635e0 |
A391403 | Triangle read by rows: T(n,k) is k-th entry of the gamma-vector of the n-dimensional cyclohedron, 0 <= k <= floor(n/2). | [
"1",
"1",
"1",
"2",
"1",
"6",
"1",
"12",
"6",
"1",
"20",
"30",
"1",
"30",
"90",
"20",
"1",
"42",
"210",
"140",
"1",
"56",
"420",
"560",
"70",
"1",
"72",
"756",
"1680",
"630",
"1",
"90",
"1260",
"4200",
"3150",
"252",
"1",
"110",
"1980",
"... | [
"nonn",
"tabf",
"easy"
] | 27 | 0 | 4 | [
"A000984",
"A002426",
"A098479",
"A105868",
"A391402",
"A391403"
] | null | Richard Ehrenborg, Dec 08 2025 | 2025-12-29T05:58:54 | oeisdata/seq/A391/A391403.seq | e8e100a13ef3ffbd85695c4561910c1d |
A391404 | Expansion of g^3/(1 + x*g), where g = 1+x*g^3 is the g.f. of A001764. | [
"1",
"2",
"9",
"41",
"205",
"1076",
"5857",
"32754",
"187056",
"1086335",
"6396041",
"38090629",
"229044178",
"1388717287",
"8480503705",
"52113795057",
"322022338699",
"1999650780743",
"12471884607292",
"78095950442235",
"490771745153602",
"3094166501849767",
"1956581175... | [
"nonn"
] | 9 | 0 | 2 | [
"A001764",
"A023053",
"A374836",
"A391178",
"A391294",
"A391404",
"A391405",
"A391406"
] | null | Seiichi Manyama, Dec 08 2025 | 2025-12-09T08:17:08 | oeisdata/seq/A391/A391404.seq | d963a301f9d582e521b88471a3646cab |
A391405 | Expansion of g^3/(1 + x*g)^2, where g = 1+x*g^3 is the g.f. of A001764. | [
"1",
"1",
"7",
"30",
"153",
"805",
"4397",
"24647",
"141020",
"820201",
"4835029",
"28823700",
"173471074",
"1052554765",
"6431805843",
"39546649026",
"244489418103",
"1518872793184",
"9477032121080",
"59364204189857",
"373178685365818",
"2353473823288829",
"1488609871298... | [
"nonn"
] | 7 | 0 | 3 | [
"A001764",
"A374836",
"A389115",
"A391174",
"A391404",
"A391405"
] | null | Seiichi Manyama, Dec 08 2025 | 2025-12-09T08:17:19 | oeisdata/seq/A391/A391405.seq | b0670dbb468b814db8cc1a8995b53cf4 |
A391406 | Expansion of g^4/(1 + x*g), where g = 1+x*g^3 is the g.f. of A001764. | [
"1",
"3",
"14",
"68",
"352",
"1895",
"10509",
"59619",
"344380",
"2018599",
"11976479",
"71786394",
"434049233",
"2644251959",
"16214959902",
"100008206636",
"619980261922",
"3861037683008",
"24144159455460",
"151540706064143",
"954348342189353",
"6028591984661431",
"3818... | [
"nonn"
] | 9 | 0 | 2 | [
"A001558",
"A001764",
"A023053",
"A391294",
"A391404",
"A391406"
] | null | Seiichi Manyama, Dec 08 2025 | 2025-12-09T08:17:15 | oeisdata/seq/A391/A391406.seq | aa6cc7c50554d0b7e19f679e4e1f52be |
A391407 | Expansion of g^4/(1 + x*g)^2, where g = 1+x*g^3 is the g.f. of A001764. | [
"1",
"2",
"11",
"52",
"271",
"1460",
"8107",
"46036",
"266134",
"1561012",
"9266929",
"55573104",
"336162522",
"2048697862",
"12567146031",
"77532920596",
"480777987559",
"2994852486212",
"18731746252378",
"117593059787784",
"740692678560938",
"4679713043486622",
"2964922... | [
"nonn"
] | 12 | 0 | 2 | [
"A001764",
"A114495",
"A374835",
"A391294",
"A391405",
"A391407"
] | null | Seiichi Manyama, Dec 08 2025 | 2025-12-09T08:17:12 | oeisdata/seq/A391/A391407.seq | 681198b608ac1d018824bc3ab05d95b3 |
A391408 | Expansion of g^5/(1 + x*g)^2, where g = 1+x*g^2 is the g.f. of A000108. | [
"1",
"3",
"11",
"38",
"133",
"468",
"1660",
"5932",
"21346",
"77301",
"281545",
"1030778",
"3791597",
"14006456",
"51941576",
"193301120",
"721697246",
"2702472854",
"10147300982",
"38197179692",
"144119279906",
"544941540968",
"2064663329656",
"7837201508508",
"29801... | [
"nonn"
] | 7 | 0 | 2 | [
"A000108",
"A065601",
"A114495",
"A389115",
"A391408"
] | null | Seiichi Manyama, Dec 08 2025 | 2025-12-09T08:17:05 | oeisdata/seq/A391/A391408.seq | 9d3199d075fbebd3c627637e1acdb905 |
A391409 | Discriminants of real quadratic fields F such that 16 is an 8th power in F_2, where F_2 is the completion of F with respect to a place above 2. | [
"8",
"28",
"56",
"60",
"92",
"120",
"124",
"136",
"156",
"184",
"188",
"220",
"248",
"264",
"284",
"312",
"316",
"328",
"348",
"376",
"380",
"412",
"440",
"444",
"456",
"476",
"508",
"520",
"568",
"572",
"584",
"604",
"632",
"636",
"668",
"696",
... | [
"nonn",
"easy",
"new"
] | 23 | 1 | 1 | [
"A003658",
"A391271",
"A391409"
] | null | Jianing Song, Jan 12 2026 | 2026-01-13T08:06:30 | oeisdata/seq/A391/A391409.seq | d63f24f1040a0fbb6aff291751b1e475 |
A391410 | Decimal expansion of the smallest positive root of P(x) = 2*x^4 + 36*x^3 - 22*x^2 - 6*x + 2. | [
"2",
"2",
"0",
"3",
"0",
"9",
"9",
"4",
"0",
"6",
"8",
"3",
"4",
"7",
"8",
"5",
"7",
"5",
"3",
"5",
"9",
"6",
"2",
"1",
"1",
"2",
"4",
"8",
"6",
"4",
"0",
"5",
"1",
"0",
"7",
"1",
"1",
"2",
"3",
"5",
"7",
"8",
"1",
"5",
"2",
"... | [
"nonn",
"cons"
] | 7 | 0 | 1 | [
"A389416",
"A391410"
] | null | Hugo Pfoertner, Dec 09 2025 | 2025-12-09T16:47:24 | oeisdata/seq/A391/A391410.seq | d933a8dc0da8619a7fc2d3795b1d7fc2 |
A391411 | First of 3 consecutive primes p1 < p2 < p3 such that the pattern of differences [p2-p1, p3-p2] does not occur earlier. | [
"2",
"3",
"5",
"7",
"19",
"23",
"29",
"31",
"47",
"83",
"89",
"109",
"113",
"137",
"139",
"197",
"199",
"211",
"241",
"283",
"317",
"331",
"359",
"397",
"401",
"463",
"467",
"503",
"509",
"521",
"523",
"619",
"691",
"773",
"787",
"883",
"887",
... | [
"nonn"
] | 30 | 1 | 1 | [
"A002386",
"A096265",
"A391411",
"A391412",
"A391413"
] | null | Hugo Pfoertner, Dec 09 2025 | 2025-12-10T17:01:10 | oeisdata/seq/A391/A391411.seq | f93e1d0327c3e25c48102130f2f043bd |
A391412 | Middle of 3 consecutive primes p1 < p2 < p3 such that the pattern of differences [p2-p1, p3-p2] does not occur earlier. | [
"3",
"5",
"7",
"11",
"23",
"29",
"31",
"37",
"53",
"89",
"97",
"113",
"127",
"139",
"149",
"199",
"211",
"223",
"251",
"293",
"331",
"337",
"367",
"401",
"409",
"467",
"479",
"509",
"521",
"523",
"541",
"631",
"701",
"787",
"797",
"887",
"907",... | [
"nonn"
] | 20 | 1 | 1 | [
"A151800",
"A391411",
"A391412",
"A391413"
] | null | Hugo Pfoertner, Dec 09 2025 | 2025-12-11T12:35:42 | oeisdata/seq/A391/A391412.seq | 07456fd2f3d2aa869db0d00cf5e1f3ab |
A391413 | Last of 3 consecutive primes p1 < p2 < p3 such that the pattern of differences [p2-p1, p3-p2] does not occur earlier. | [
"5",
"7",
"11",
"13",
"29",
"31",
"37",
"41",
"59",
"97",
"101",
"127",
"131",
"149",
"151",
"211",
"223",
"227",
"257",
"307",
"337",
"347",
"373",
"409",
"419",
"479",
"487",
"521",
"523",
"541",
"547",
"641",
"709",
"797",
"809",
"907",
"911... | [
"nonn"
] | 26 | 1 | 1 | [
"A151800",
"A391411",
"A391412",
"A391413"
] | null | Hugo Pfoertner, Dec 09 2025 | 2025-12-11T15:23:23 | oeisdata/seq/A391/A391413.seq | dd05c815b3f513587d87b45697b6d7a7 |
A391414 | a(n) is the median of the set of the distinct values of (n-1)^n, (n-1)^(n+1), n^(n-1), n^(n+1), (n+1)^(n-1), (n+1)^n. | [
"1",
"3",
"16",
"184",
"2696",
"47466",
"979776",
"23059204",
"567108864",
"14712104501",
"421504185344",
"13218256749601",
"450353989316608",
"16565151205544957",
"654244800082329600",
"27614800115689879553",
"1240529732459024678912",
"59095217374989483261925",
"2975557672677668... | [
"nonn"
] | 17 | 1 | 2 | [
"A051489",
"A062024",
"A391414"
] | null | Hugo Pfoertner, Dec 16 2025 | 2025-12-17T15:57:22 | oeisdata/seq/A391/A391414.seq | 610157dc78e480d42ee1b337ec44678b |
A391415 | Nonsquarefree numbers that are neither cubefree nor perfect powers. | [
"24",
"40",
"48",
"54",
"56",
"72",
"80",
"88",
"96",
"104",
"108",
"112",
"120",
"135",
"136",
"152",
"160",
"162",
"168",
"176",
"184",
"189",
"192",
"200",
"208",
"224",
"232",
"240",
"248",
"250",
"264",
"270",
"272",
"280",
"288",
"296",
"... | [
"nonn",
"easy"
] | 12 | 1 | 1 | [
"A004709",
"A007916",
"A013929",
"A024619",
"A046099",
"A052486",
"A126706",
"A303946",
"A362148",
"A378767",
"A389864",
"A391319",
"A391415",
"A391416"
] | null | Michael De Vlieger, Dec 13 2025 | 2025-12-27T18:06:13 | oeisdata/seq/A391/A391415.seq | 2672107ab614634137178b2357f87493 |
A391416 | Perfect powers that are neither prime powers nor cubefree. | [
"144",
"216",
"324",
"400",
"576",
"784",
"1000",
"1296",
"1600",
"1728",
"1936",
"2025",
"2304",
"2500",
"2704",
"2744",
"2916",
"3136",
"3375",
"3600",
"3969",
"4624",
"5184",
"5625",
"5776",
"5832",
"6400",
"7056",
"7744",
"7776",
"8000",
"8100",
"8... | [
"nonn",
"easy"
] | 19 | 1 | 1 | [
"A001597",
"A001694",
"A013929",
"A024619",
"A046099",
"A052486",
"A072102",
"A082020",
"A085548",
"A126706",
"A131605",
"A177492",
"A246547",
"A286708",
"A383394",
"A386762",
"A388304",
"A389864",
"A391416"
] | null | Michael De Vlieger, Dec 13 2025 | 2025-12-21T03:12:50 | oeisdata/seq/A391/A391416.seq | d8f4863b498d23ecdd5bb12e80fbf826 |
A391417 | Discriminants of real quadratic fields whose class group is isomorphic to (C_2)^r, r >= 0. | [
"5",
"8",
"12",
"13",
"17",
"21",
"24",
"28",
"29",
"33",
"37",
"40",
"41",
"44",
"53",
"56",
"57",
"60",
"61",
"65",
"69",
"73",
"76",
"77",
"85",
"88",
"89",
"92",
"93",
"97",
"101",
"104",
"105",
"109",
"113",
"120",
"124",
"129",
"133",... | [
"nonn"
] | 17 | 1 | 1 | [
"A003658",
"A079896",
"A087048",
"A317989",
"A317990",
"A317991",
"A317992",
"A390079",
"A391417",
"A391419",
"A391422",
"A391426",
"A391435",
"A391436",
"A391437",
"A391438",
"A391439",
"A391440",
"A391441"
] | null | Jianing Song, Dec 09 2025 | 2025-12-09T22:06:56 | oeisdata/seq/A391/A391417.seq | 12c8ef26484b9f09ba9cc7cbb5534152 |
A391418 | Class number of order of real quadratic fields with discriminant D = A079896(n). | [
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"2",
"2",
"1",
"1",
"... | [
"nonn"
] | 11 | 1 | 14 | [
"A003646",
"A003652",
"A003655",
"A003656",
"A003658",
"A079896",
"A087048",
"A094612",
"A094619",
"A133315",
"A344408",
"A344409",
"A390079",
"A391418",
"A391420",
"A391421",
"A391423",
"A391424",
"A391425"
] | null | Jianing Song, Dec 09 2025 | 2025-12-10T06:54:04 | oeisdata/seq/A391/A391418.seq | ce84882a8bc02c50f66489135cfb9205 |
A391419 | Discriminants of orders of real quadratic fields whose class group is isomorphic to (C_2)^r, r >= 0. | [
"5",
"8",
"12",
"13",
"17",
"20",
"21",
"24",
"28",
"29",
"32",
"33",
"37",
"40",
"41",
"44",
"45",
"48",
"52",
"53",
"56",
"57",
"60",
"61",
"65",
"68",
"69",
"72",
"73",
"76",
"77",
"80",
"84",
"85",
"88",
"89",
"92",
"93",
"96",
"97",
... | [
"nonn"
] | 14 | 1 | 1 | [
"A003658",
"A079896",
"A087048",
"A317989",
"A317990",
"A317991",
"A317992",
"A390079",
"A391417",
"A391419",
"A391422",
"A391426",
"A391435",
"A391436",
"A391437",
"A391438",
"A391439",
"A391440",
"A391441"
] | null | Jianing Song, Dec 09 2025 | 2025-12-09T22:06:50 | oeisdata/seq/A391/A391419.seq | a164183a11c76fd5bcc1249a13fbd4a7 |
A391420 | Discriminants of real quadratic fields with form class number 2. | [
"12",
"21",
"24",
"28",
"33",
"40",
"44",
"56",
"57",
"65",
"69",
"76",
"77",
"85",
"88",
"92",
"93",
"104",
"124",
"129",
"133",
"141",
"152",
"161",
"172",
"177",
"184",
"185",
"188",
"201",
"209",
"213",
"217",
"232",
"236",
"237",
"248",
... | [
"nonn"
] | 12 | 1 | 1 | [
"A003646",
"A003652",
"A003655",
"A003656",
"A003658",
"A014077",
"A079896",
"A087048",
"A094612",
"A094619",
"A133315",
"A327297",
"A344408",
"A344409",
"A390079",
"A391418",
"A391420",
"A391421",
"A391423",
"A391424",
"A391425"
] | null | Jianing Song, Dec 09 2025 | 2025-12-10T06:53:56 | oeisdata/seq/A391/A391420.seq | cd6b19cbce8c13e3ca67138a8861ba71 |
A391421 | Discriminants of real quadratic fields with form class number 3. | [
"229",
"257",
"733",
"761",
"1229",
"1373",
"1489",
"1901",
"2089",
"2213",
"2557",
"2677",
"2713",
"2777",
"2857",
"2917",
"3221",
"3229",
"3877",
"3889",
"4001",
"4481",
"4493",
"4597",
"4649",
"4729",
"4933",
"5081",
"5261",
"5281",
"5297",
"5333",
... | [
"nonn"
] | 13 | 1 | 1 | [
"A003646",
"A003652",
"A003655",
"A003656",
"A003658",
"A014077",
"A079896",
"A087048",
"A094612",
"A094619",
"A133315",
"A344408",
"A344409",
"A390079",
"A391418",
"A391420",
"A391421",
"A391423",
"A391424",
"A391425"
] | null | Jianing Song, Dec 09 2025 | 2025-12-10T13:42:20 | oeisdata/seq/A391/A391421.seq | 2bf805dc6c062df5b6d750bbdafe380a |
A391422 | Discriminants of real quadratic fields with 1 class per genus. | [
"5",
"8",
"12",
"13",
"17",
"21",
"24",
"28",
"29",
"33",
"37",
"40",
"41",
"44",
"53",
"56",
"57",
"60",
"61",
"65",
"69",
"73",
"76",
"77",
"85",
"88",
"89",
"92",
"93",
"97",
"101",
"104",
"105",
"109",
"113",
"120",
"124",
"129",
"133",... | [
"nonn"
] | 15 | 1 | 1 | [
"A003658",
"A079896",
"A087048",
"A317989",
"A317990",
"A317991",
"A317992",
"A390079",
"A391417",
"A391419",
"A391422",
"A391426",
"A391435",
"A391436",
"A391437",
"A391438",
"A391439",
"A391440",
"A391441"
] | null | Jianing Song, Dec 09 2025 | 2025-12-09T22:07:49 | oeisdata/seq/A391/A391422.seq | bb19b3a99fcbd03ac67a531e5abe1ed0 |
A391423 | Positive discriminants of orders of quadratic fields with form class number 1. | [
"5",
"8",
"13",
"17",
"20",
"29",
"37",
"41",
"52",
"53",
"61",
"68",
"73",
"89",
"97",
"101",
"109",
"113",
"116",
"125",
"137",
"149",
"157",
"164",
"173",
"181",
"193",
"197",
"212",
"233",
"241",
"244",
"269",
"277",
"281",
"292",
"293",
... | [
"nonn"
] | 14 | 1 | 1 | [
"A003646",
"A003652",
"A003655",
"A003656",
"A003658",
"A079896",
"A087048",
"A094612",
"A094619",
"A133315",
"A306638",
"A344408",
"A344409",
"A390079",
"A391418",
"A391420",
"A391421",
"A391423",
"A391424",
"A391425"
] | null | Jianing Song, Dec 09 2025 | 2025-12-10T06:53:52 | oeisdata/seq/A391/A391423.seq | 9ed88b2951f0d71ac6f350e12529679c |
A391424 | Positive discriminants of orders of quadratic fields with form class number 2. | [
"12",
"21",
"24",
"28",
"32",
"33",
"40",
"44",
"45",
"48",
"56",
"57",
"65",
"69",
"72",
"76",
"77",
"80",
"84",
"85",
"88",
"92",
"93",
"104",
"108",
"112",
"117",
"124",
"128",
"129",
"132",
"133",
"141",
"152",
"153",
"161",
"172",
"176",... | [
"nonn"
] | 13 | 1 | 1 | [
"A003646",
"A003652",
"A003655",
"A003656",
"A003658",
"A079896",
"A087048",
"A094612",
"A094619",
"A133315",
"A306638",
"A344408",
"A344409",
"A390079",
"A391418",
"A391420",
"A391421",
"A391423",
"A391424",
"A391425"
] | null | Jianing Song, Dec 09 2025 | 2025-12-10T06:53:47 | oeisdata/seq/A391/A391424.seq | 67994821743f03490406f04b14c0728f |
A391425 | Positive discriminants of orders of quadratic fields with form class number 3. | [
"148",
"229",
"257",
"404",
"733",
"761",
"788",
"916",
"1028",
"1076",
"1229",
"1373",
"1396",
"1489",
"1492",
"1556",
"1901",
"2089",
"2213",
"2228",
"2557",
"2677",
"2708",
"2713",
"2777",
"2804",
"2836",
"2857",
"2917",
"2932",
"3028",
"3044",
"322... | [
"nonn"
] | 15 | 1 | 1 | [
"A003646",
"A003652",
"A003655",
"A003656",
"A003658",
"A079896",
"A087048",
"A094612",
"A094619",
"A133315",
"A306638",
"A344408",
"A344409",
"A390079",
"A391418",
"A391420",
"A391421",
"A391423",
"A391424",
"A391425"
] | null | Jianing Song, Dec 09 2025 | 2025-12-10T10:36:25 | oeisdata/seq/A391/A391425.seq | 4da8839b339952fe6142cb890f197412 |
A391426 | Number of elements that square to the identity in the class group of real quadratic field with discriminant A003658(n), n >= 2. | [
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"... | [
"nonn"
] | 13 | 2 | 12 | [
"A003640",
"A003658",
"A079896",
"A087048",
"A317989",
"A317990",
"A317991",
"A317992",
"A390079",
"A391417",
"A391419",
"A391422",
"A391426",
"A391435",
"A391436",
"A391437",
"A391438",
"A391439",
"A391440",
"A391441"
] | null | Jianing Song, Dec 09 2025 | 2025-12-10T06:53:38 | oeisdata/seq/A391/A391426.seq | b41d0c6747807009b6d91cb2a65661a1 |
A391427 | Cubefree exponential abundant numbers: cubefree numbers k for which A051377(k) > 2*k. | [
"900",
"1764",
"4356",
"4900",
"6084",
"6300",
"8820",
"9900",
"10404",
"11700",
"12996",
"14700",
"15300",
"17100",
"19044",
"19404",
"20700",
"21780",
"22932",
"26100",
"27900",
"29988",
"30276",
"30420",
"30492",
"33300",
"33516",
"34596",
"36900",
"38700... | [
"nonn",
"easy"
] | 10 | 1 | 1 | [
"A001694",
"A004709",
"A005117",
"A051377",
"A059956",
"A064987",
"A087248",
"A129575",
"A357695",
"A386798",
"A391427",
"A391428",
"A391429",
"A391430"
] | null | Amiram Eldar, Dec 09 2025 | 2025-12-10T08:39:08 | oeisdata/seq/A391/A391427.seq | d97b02169b9f6dbebf517122d47b919d |
A391428 | Exponential abundant numbers that are squares of squarefree numbers. | [
"900",
"1764",
"4356",
"4900",
"6084",
"10404",
"12996",
"19044",
"30276",
"34596",
"44100",
"49284",
"60516",
"66564",
"79524",
"101124",
"108900",
"125316",
"133956",
"152100",
"161604",
"181476",
"191844",
"213444",
"224676",
"248004",
"260100",
"285156",
"... | [
"nonn",
"easy"
] | 7 | 1 | 1 | [
"A000290",
"A001694",
"A062503",
"A087248",
"A129575",
"A390558",
"A391427",
"A391428",
"A391430"
] | null | Amiram Eldar, Dec 09 2025 | 2025-12-10T08:38:29 | oeisdata/seq/A391/A391428.seq | 90e5b82eb22d63a694ace46d92af6c8c |
A391429 | Odd cubefree exponential abundant numbers: odd cubefree numbers k for which A051377(k) > 2*k. | [
"225450225",
"385533225",
"481583025",
"538472025",
"672624225",
"705699225",
"985646025",
"1121915025",
"1150227225",
"1281998025",
"1566972225",
"1685513025",
"1790559225",
"1826280225",
"2105433225",
"2242496025",
"2466612225",
"2550755025",
"2679615225",
"2946861225",
"31... | [
"nonn",
"easy"
] | 9 | 1 | 1 | [
"A004709",
"A005117",
"A005408",
"A051377",
"A056911",
"A059956",
"A064987",
"A112643",
"A129575",
"A321147",
"A357695",
"A357697",
"A381822",
"A391427",
"A391429",
"A391430"
] | null | Amiram Eldar, Dec 09 2025 | 2025-12-10T08:38:50 | oeisdata/seq/A391/A391429.seq | 72521311b40bc5f84bf5ce6d74a73713 |
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