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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
A391895 | a(n) = Sum_{k=0..n} (k+1) * 2^k * binomial(2*k+1,2*n-2*k). | [
"1",
"4",
"24",
"152",
"812",
"4192",
"21312",
"106048",
"519568",
"2516672",
"12074112",
"57467008",
"271692992",
"1277193216",
"5974321152",
"27825801216",
"129109422336",
"597042549760",
"2752617871360",
"12656462034944",
"58052075088896",
"265680602210304",
"121345414... | [
"nonn"
] | 14 | 0 | 2 | [
"A390700",
"A391832",
"A391894",
"A391895"
] | null | Seiichi Manyama, Dec 22 2025 | 2026-01-01T08:46:39 | oeisdata/seq/A391/A391895.seq | 9e8a475676ef1f412f1aa15ab5c30e09 |
A391896 | Cubefull numbers with exactly 2 distinct prime factors. | [
"216",
"432",
"648",
"864",
"1000",
"1296",
"1728",
"1944",
"2000",
"2592",
"2744",
"3375",
"3456",
"3888",
"4000",
"5000",
"5184",
"5488",
"5832",
"6912",
"7776",
"8000",
"9261",
"10000",
"10125",
"10368",
"10648",
"10976",
"11664",
"13824",
"15552",
"1... | [
"nonn",
"easy"
] | 10 | 1 | 1 | [
"A001694",
"A007774",
"A013929",
"A024619",
"A036966",
"A046099",
"A126706",
"A200511",
"A286708",
"A355462",
"A372404",
"A372695",
"A376936",
"A378767",
"A391896"
] | null | Michael De Vlieger, Dec 23 2025 | 2025-12-24T04:11:06 | oeisdata/seq/A391/A391896.seq | 9b160f53d7c7639799a1e36888bed16c |
A391897 | Partial products of A063659. | [
"1",
"2",
"6",
"18",
"90",
"540",
"3780",
"22680",
"181440",
"1814400",
"19958400",
"179625600",
"2335132800",
"32691859200",
"490377888000",
"5884534656000",
"100037089152000",
"1600593426432000",
"30411275102208000",
"456169126533120000",
"9579551657195520000",
"210750136... | [
"nonn",
"easy"
] | 7 | 1 | 2 | [
"A001088",
"A001615",
"A059381",
"A059382",
"A059383",
"A059384",
"A063659",
"A066780",
"A066843",
"A130779",
"A175596",
"A175836",
"A239672",
"A321613",
"A322175",
"A391897"
] | null | Amiram Eldar, Dec 23 2025 | 2025-12-23T04:22:15 | oeisdata/seq/A391/A391897.seq | b654144f7a244e693bceacce9bfe2b70 |
A391898 | The maximum exponent in the prime factorization of the exponentially noncomposite numbers (A390439). | [
"0",
"1",
"1",
"2",
"1",
"1",
"1",
"3",
"2",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"3",
"2",
"1",
"3",
"2",
"1",
"1",
"1",
"5",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"2",
"2",
"1",
"... | [
"nonn",
"easy"
] | 12 | 1 | 4 | [
"A051903",
"A375766",
"A375768",
"A390439",
"A391898",
"A391899"
] | null | Amiram Eldar, Dec 23 2025 | 2025-12-23T04:47:50 | oeisdata/seq/A391/A391898.seq | d5eee8452b300c0250c1627afdb436b7 |
A391899 | The maximum exponent in the prime factorization of the exponentially squarefree numbers (A209061). | [
"0",
"1",
"1",
"2",
"1",
"1",
"1",
"3",
"2",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"3",
"2",
"1",
"3",
"2",
"1",
"1",
"1",
"5",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"2",
"2",
"1",
"... | [
"nonn",
"easy"
] | 11 | 1 | 4 | [
"A008683",
"A051903",
"A209061",
"A262276",
"A375766",
"A375768",
"A391898",
"A391899"
] | null | Amiram Eldar, Dec 23 2025 | 2025-12-23T04:47:55 | oeisdata/seq/A391/A391899.seq | 2771c824e121fa5aed51aeacc8108e51 |
A391900 | The total number of prime factors (counted with multiplicity) of the prime factorization exponents of n. | [
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"1",
"0",
"0",
"1",
"0",
"0",
"0",
"2",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"2",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"1",
"... | [
"nonn",
"easy"
] | 8 | 1 | 16 | [
"A001222",
"A005361",
"A071325",
"A362412",
"A366073",
"A376657",
"A386262",
"A389836",
"A391900"
] | null | Amiram Eldar, Dec 23 2025 | 2025-12-23T04:20:49 | oeisdata/seq/A391/A391900.seq | e77014a67f59db63a5b95ebde0b17307 |
A391901 | The number of distinct factorials that are unitarily dividing n. | [
"1",
"2",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"... | [
"nonn",
"easy"
] | 9 | 1 | 2 | [
"A000010",
"A000142",
"A048855",
"A055881",
"A077610",
"A123476",
"A373318",
"A373319",
"A391901"
] | null | Amiram Eldar, Dec 23 2025 | 2025-12-23T04:20:25 | oeisdata/seq/A391/A391901.seq | 7398bfa5caf83f7dbdcea548e5fd40e4 |
A391902 | a(n) = Sum_{k=0..n} binomial(3*k,3*(n-k)). | [
"1",
"1",
"2",
"21",
"86",
"305",
"1381",
"6042",
"24901",
"105364",
"450017",
"1902321",
"8044478",
"34114553",
"144535714",
"612041073",
"2592800365",
"10984222558",
"46527959417",
"197093207976",
"834913179137",
"3536745086753",
"14981831303770",
"63464151953133",
... | [
"nonn"
] | 19 | 0 | 3 | [
"A003522",
"A391902",
"A391903",
"A391904"
] | null | Seiichi Manyama, Dec 23 2025 | 2026-01-01T03:01:43 | oeisdata/seq/A391/A391902.seq | b28943fc60928936c202b20ab9320f8e |
A391903 | a(n) = Sum_{k=0..floor(n/2)} binomial(3*k,3*(n-2*k)). | [
"1",
"0",
"1",
"1",
"1",
"20",
"2",
"84",
"85",
"221",
"925",
"675",
"5007",
"5821",
"19020",
"49951",
"72829",
"296770",
"428528",
"1364693",
"3001497",
"5998390",
"18112232",
"31698490",
"92287620",
"193987770",
"443261263",
"1145617890",
"2292692419",
"61... | [
"nonn"
] | 18 | 0 | 6 | [
"A391902",
"A391903",
"A391904"
] | null | Seiichi Manyama, Dec 23 2025 | 2025-12-31T04:14:46 | oeisdata/seq/A391/A391903.seq | 13b1888eed47fbb01566f5e156e4e883 |
A391904 | a(n) = Sum_{k=0..floor(n/3)} binomial(3*k,3*(n-3*k)). | [
"1",
"0",
"0",
"1",
"1",
"0",
"1",
"20",
"1",
"1",
"84",
"84",
"2",
"220",
"924",
"221",
"456",
"5005",
"5006",
"1271",
"18565",
"48621",
"19894",
"55080",
"293932",
"295954",
"188860",
"1308835",
"2707082",
"1603514",
"4821422",
"17389944",
"17977636"... | [
"nonn"
] | 18 | 0 | 8 | [
"A391902",
"A391903",
"A391904"
] | null | Seiichi Manyama, Dec 23 2025 | 2025-12-31T04:14:49 | oeisdata/seq/A391/A391904.seq | 40acc9afa7dd1db8a3fa79b21d94a032 |
A391905 | Numbers which are the hypotenuse of a primitive Pythagorean quadruple whose legs are also members of a smaller primitive Pythagorean quadruple. | [
"49",
"137",
"161",
"245",
"257",
"497",
"637",
"685",
"805",
"833",
"1169",
"1225",
"1285",
"1421",
"1513",
"1601",
"1781",
"1813",
"1897",
"1993",
"2009",
"2093",
"2329",
"2369",
"2485",
"2597",
"2681",
"2737",
"2777",
"2989",
"3185",
"3209",
"3281",... | [
"nonn"
] | 11 | 1 | 1 | [
"A256418",
"A391905"
] | null | Charles L. Hohn, Dec 23 2025 | 2025-12-30T19:52:12 | oeisdata/seq/A391/A391905.seq | d0369cf181c731b23f8f707f17245495 |
A391906 | Numerators of the convergents given by treating A390946 as continued fraction coefficients after the leading 0. | [
"1",
"2",
"5",
"12",
"17",
"29",
"75",
"254",
"583",
"1420",
"4843",
"6263",
"17369",
"41001",
"222374",
"485749",
"1679621",
"2165370",
"6010361",
"14186092",
"76940821",
"91126913",
"168067734",
"259194647",
"945651675",
"5933104697",
"12811861069",
"571805489... | [
"nonn",
"frac"
] | 6 | 1 | 2 | [
"A086702",
"A390946",
"A391906",
"A391907"
] | null | Jwalin Bhatt, Dec 23 2025 | 2025-12-29T20:25:07 | oeisdata/seq/A391/A391906.seq | e1a7c6331fab0327a872e11db9675726 |
A391907 | Denominators of the convergents given by treating A390946 as continued fraction coefficients after the leading 0. | [
"1",
"3",
"7",
"17",
"24",
"41",
"106",
"359",
"824",
"2007",
"6845",
"8852",
"24549",
"57950",
"314299",
"686548",
"2373943",
"3060491",
"8494925",
"20050341",
"108746630",
"128796971",
"237543601",
"366340572",
"1336565317",
"8385732474",
"18108030265",
"80817... | [
"nonn",
"frac"
] | 6 | 1 | 2 | [
"A086702",
"A390946",
"A391906",
"A391907"
] | null | Jwalin Bhatt, Dec 23 2025 | 2025-12-29T20:25:45 | oeisdata/seq/A391/A391907.seq | 5e617520a871976d994fe959495a60d2 |
A391908 | Numbers k such that sigma(k) = psi(k) + phi(k) + omega(k)^5. | [
"1984",
"2760",
"24852",
"36084",
"49044",
"57088",
"245248",
"377910",
"1014784",
"11507958",
"16350500",
"151632054",
"170747262",
"246570534",
"463572774",
"1011059264",
"2035069974",
"7980282656"
] | [
"nonn",
"hard",
"more"
] | 15 | 1 | 1 | [
"A000010",
"A000203",
"A001221",
"A001615",
"A390049",
"A391312",
"A391749",
"A391763",
"A391908"
] | null | S. I. Dimitrov, Dec 23 2025 | 2025-12-29T21:43:27 | oeisdata/seq/A391/A391908.seq | d3dce224c1c97c9a3813912fce1e5a6a |
A391909 | Numbers k such that -1 <= A195017(k) <= 1. | [
"1",
"2",
"3",
"5",
"6",
"7",
"11",
"12",
"13",
"14",
"15",
"17",
"18",
"19",
"23",
"26",
"28",
"29",
"30",
"31",
"33",
"35",
"36",
"37",
"38",
"41",
"42",
"43",
"45",
"47",
"51",
"52",
"53",
"58",
"59",
"61",
"65",
"66",
"67",
"69",
"7... | [
"nonn",
"easy",
"new"
] | 20 | 1 | 2 | [
"A000040",
"A073485",
"A195017",
"A206284",
"A257991",
"A257992",
"A260442",
"A260443",
"A297845",
"A325698",
"A391746",
"A391747",
"A391909"
] | null | Antti Karttunen and Peter Munn, Dec 23 2025 | 2026-01-04T23:27:18 | oeisdata/seq/A391/A391909.seq | a391fce9cd18a7893d61e6bd743aa500 |
A391910 | Triangle read by rows: T(n,k) are the unique integer coefficients such that Sum_{k=0..n} T(n,k)*A125790(k,m)/2^(n*k) = (m+2)^n for all n >= 0, m >= 0. | [
"1",
"1",
"2",
"1",
"8",
"16",
"1",
"26",
"192",
"384",
"1",
"80",
"1696",
"12288",
"24576",
"1",
"242",
"13440",
"272640",
"1966080",
"3932160",
"1",
"728",
"101296",
"5222400",
"104816640",
"754974720",
"1509949440",
"1",
"2186",
"743232",
"92663424",
... | [
"nonn",
"tabl",
"changed"
] | 15 | 0 | 3 | [
"A000120",
"A125790",
"A391910"
] | null | Mikhail Kurkov, Dec 23 2025 | 2026-01-17T16:33:17 | oeisdata/seq/A391/A391910.seq | 87af263cae983068c17391e40794e13b |
A391911 | Dimension of the space of twist-minimal newforms of weight 2 and level n. | [
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"1",
"1",
"0",
"1",
"0",
"1",
"1",
"1",
"0",
"2",
"1",
"0",
"2",
"1",
"0",
"2",
"1",
"2",
"1",
"1",
"1",
"3",
"1",
"2",
"2",
"3",
"1",
"3",
"1",
"3",
"1",
"0",
"... | [
"nonn"
] | 16 | 1 | 23 | [
"A001617",
"A127788",
"A391911"
] | null | Andrew R. Booker, Dec 23 2025 | 2025-12-29T23:10:26 | oeisdata/seq/A391/A391911.seq | 35bc2b3cdb0abaeabbb1b0d7642ffa0d |
A391912 | Number of irredundant sets in the n-triangular honeycomb queen graph. | [
"2",
"4",
"22",
"76",
"454",
"3040",
"23077",
"202644",
"2006095",
"22326039"
] | [
"nonn",
"more",
"changed"
] | 8 | 1 | 1 | null | null | Eric W. Weisstein, Dec 23 2025 | 2026-01-18T18:00:09 | oeisdata/seq/A391/A391912.seq | 0241bfd997c312af015b47dfe8a73897 |
A391913 | Number of irredundant sets in the Lingren-Sousslier graph on 6n+4 vertices. | [
"253",
"5517",
"124383",
"2860318"
] | [
"nonn",
"more"
] | 4 | 1 | 1 | null | null | Eric W. Weisstein, Dec 23 2025 | 2025-12-23T09:40:49 | oeisdata/seq/A391/A391913.seq | 250ddf1c8a08b6eec2d36b62af68b6c2 |
A391914 | Number of irredundant sets in the n-Lucas cube graph. | [
"2",
"5",
"9",
"49",
"320",
"10713",
"2256637"
] | [
"nonn",
"more"
] | 4 | 1 | 1 | null | null | Eric W. Weisstein, Dec 23 2025 | 2025-12-23T09:40:53 | oeisdata/seq/A391/A391914.seq | b303308f23a849ae34cf04c5e27bdfd7 |
A391915 | Number of irredundant sets in the n-Pell graph. | [
"3",
"16",
"544",
"2220016"
] | [
"nonn",
"more"
] | 4 | 1 | 1 | null | null | Eric W. Weisstein, Dec 23 2025 | 2025-12-23T09:41:02 | oeisdata/seq/A391/A391915.seq | 7d2933647322b747fe35d512854f9893 |
A391916 | Number of irredundant sets in the n-trapezohedral graph. | [
"77",
"192",
"523",
"1389",
"3718",
"10048",
"27377",
"75239",
"208502",
"582141",
"1636305",
"4626548",
"13148533",
"37534128",
"107557937",
"309242349",
"891663491",
"2577397759",
"7466156079",
"21668293968",
"62988073938",
"183360687221",
"534427741078",
"15593286198... | [
"nonn"
] | 13 | 3 | 1 | [
"A370089",
"A391916"
] | null | Eric W. Weisstein, Dec 23 2025 | 2026-01-01T15:49:09 | oeisdata/seq/A391/A391916.seq | 3e2f500cd7e89d22a63626afd74c9f7c |
A391917 | Number of irredundant sets in the n-double cone graph. | [
"2",
"10",
"17",
"122",
"257",
"577",
"1850",
"5626",
"16901",
"47525",
"140626",
"414737",
"1223237",
"3583450",
"10523537",
"30946970",
"90973445",
"267322501",
"785456677",
"2308418117",
"6784157957",
"19937157602",
"58589654810",
"172181842705",
"506006018282",
... | [
"nonn",
"easy",
"changed"
] | 24 | 1 | 1 | [
"A290493",
"A290494",
"A391917",
"A392237"
] | null | Eric W. Weisstein, Dec 23 2025 | 2026-01-08T13:48:52 | oeisdata/seq/A391/A391917.seq | 39572bf54ae3012963debc0ab79617bf |
A391918 | Number of irredundant sets in the n-triangular honeycomb acute knight graph. | [
"2",
"8",
"27",
"144",
"1331",
"27000",
"569344",
"16777216",
"1083206683",
"85307250648",
"9197641041408",
"1896999488202671",
"567844742926891708"
] | [
"nonn",
"more"
] | 4 | 1 | 1 | null | null | Eric W. Weisstein, Dec 23 2025 | 2025-12-23T09:34:21 | oeisdata/seq/A391/A391918.seq | a10234d26c00328c5e9f4ed87bd64419 |
A391920 | Simple continued fraction expansion of (Pi - e*log(Pi))/(log(Pi) - 1). | [
"0",
"4",
"1",
"5",
"3",
"3",
"1",
"1",
"1",
"2",
"15",
"1",
"3",
"1",
"1",
"21",
"1",
"10",
"14",
"1",
"3",
"2",
"2",
"2",
"1",
"16",
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"2",
"1",
"37",
"1",
"2",
"12",
"3",
"4",
"2",
"3",
"2",
"... | [
"nonn",
"cofr",
"easy"
] | 10 | 0 | 2 | [
"A001203",
"A003417",
"A259671",
"A380965",
"A391920"
] | null | Stefano Spezia, Dec 23 2025 | 2025-12-25T06:03:51 | oeisdata/seq/A391/A391920.seq | 729e0d3280fe5fb4e0bde5e7fb973a1a |
A391921 | Powerful numbers that are not cubefree and are divisible by exactly 2 distinct primes. | [
"72",
"108",
"144",
"200",
"216",
"288",
"324",
"392",
"400",
"432",
"500",
"576",
"648",
"675",
"784",
"800",
"864",
"968",
"972",
"1000",
"1125",
"1152",
"1296",
"1323",
"1352",
"1372",
"1568",
"1600",
"1728",
"1936",
"1944",
"2000",
"2025",
"2304"... | [
"nonn",
"easy",
"new"
] | 12 | 1 | 1 | [
"A001694",
"A007774",
"A024619",
"A046099",
"A126706",
"A286708",
"A355462",
"A372404",
"A378767",
"A391896",
"A391921"
] | null | Michael De Vlieger, Dec 23 2025 | 2026-01-06T11:11:10 | oeisdata/seq/A391/A391921.seq | 647886c110ec5c65a917cf8e1bee550d |
A391922 | Numbers that are neither cubefree nor powerful and have exactly 2 distinct prime factors. | [
"24",
"40",
"48",
"54",
"56",
"80",
"88",
"96",
"104",
"112",
"135",
"136",
"152",
"160",
"162",
"176",
"184",
"189",
"192",
"208",
"224",
"232",
"248",
"250",
"272",
"296",
"297",
"304",
"320",
"328",
"344",
"351",
"352",
"368",
"375",
"376",
... | [
"nonn",
"new"
] | 11 | 1 | 1 | [
"A007774",
"A013929",
"A046099",
"A054753",
"A126706",
"A200511",
"A332785",
"A345381",
"A378767",
"A391319",
"A391922"
] | null | Michael De Vlieger, Dec 23 2025 | 2026-01-17T23:10:55 | oeisdata/seq/A391/A391922.seq | cf644c5d741ec7a5b60ef270f7f11a52 |
A391923 | Achilles numbers divisible by only 1 cube greater than 1. | [
"72",
"108",
"200",
"288",
"392",
"500",
"675",
"800",
"968",
"972",
"1125",
"1152",
"1323",
"1352",
"1372",
"1568",
"1800",
"2312",
"2700",
"2888",
"3087",
"3200",
"3267",
"3528",
"3872",
"4232",
"4500",
"4563",
"4608",
"5292",
"5324",
"5408",
"6075",... | [
"nonn",
"easy"
] | 17 | 1 | 1 | [
"A001694",
"A013929",
"A024619",
"A052486",
"A082020",
"A126706",
"A286708",
"A369632",
"A390539",
"A391923",
"A391968"
] | null | Michael De Vlieger, Dec 25 2025 | 2026-01-04T10:44:44 | oeisdata/seq/A391/A391923.seq | 8c439df7d8906d03475682b3bc2a38e0 |
A391924 | Numbers k such that (26^k - 5^k)/21 is prime. | [
"2",
"79",
"2621",
"21841"
] | [
"nonn",
"hard",
"more"
] | 5 | 1 | 1 | [
"A062587",
"A062589",
"A127996",
"A127997",
"A128344",
"A204940",
"A217320",
"A225807",
"A229542",
"A375161",
"A375236",
"A377031",
"A391924"
] | null | Robert Price, Dec 23 2025 | 2025-12-23T14:01:54 | oeisdata/seq/A391/A391924.seq | 4e2bffafbefd042eb620826e1149f2b8 |
A391925 | Square array read by descending antidiagonals: A(n, k) is the k-th natural number i that satisfies i*n = A048720(i,m) for some m, where A048720 is carryless base-2 multiplication. | [
"1",
"2",
"1",
"3",
"2",
"1",
"4",
"3",
"2",
"1",
"5",
"4",
"3",
"2",
"1",
"6",
"5",
"4",
"3",
"2",
"1",
"7",
"6",
"5",
"4",
"3",
"2",
"1",
"8",
"7",
"6",
"5",
"4",
"3",
"2",
"1",
"9",
"8",
"7",
"6",
"6",
"4",
"4",
"2",
"1",
"... | [
"nonn",
"base",
"tabl"
] | 27 | 1 | 2 | [
"A000012",
"A001477",
"A048720",
"A065621",
"A115872",
"A391585",
"A391725",
"A391740",
"A391742",
"A391744",
"A391846",
"A391848",
"A391850",
"A391852",
"A391854",
"A391856",
"A391858",
"A391860",
"A391925",
"A391926"
] | null | Antti Karttunen, Dec 23 2025 | 2025-12-23T15:27:45 | oeisdata/seq/A391/A391925.seq | 94f65750775d3667fdd4fa97a0dad4c5 |
A391926 | Square array read by descending antidiagonals: find the k-th natural number i that satisfies i*n = A048720(i,m) for some m, then A(n, k) = m. Here A048720 is carryless base-2 multiplication. | [
"1",
"1",
"2",
"1",
"2",
"3",
"1",
"2",
"3",
"4",
"1",
"2",
"7",
"4",
"5",
"1",
"2",
"3",
"4",
"5",
"6",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"1",
"2",
"7",
"4",
"5",
"14",
"7",
"8",
"1",
"2",
"7",
"4",
"5",
"6",
"7",
"8",
"9",
... | [
"nonn",
"base",
"tabl"
] | 21 | 1 | 3 | [
"A000012",
"A000027",
"A000120",
"A048720",
"A280500",
"A391726",
"A391925",
"A391926"
] | null | Antti Karttunen, Dec 23 2025 | 2025-12-29T15:08:48 | oeisdata/seq/A391/A391926.seq | 0f6ebce1c21980f20aeff20fc779fba3 |
A391927 | Numbers k for which A373842(k) >= k, where A373842 is the arithmetic derivative of the primorial base log-function. | [
"5",
"7",
"11",
"13",
"17",
"19",
"21",
"23",
"28",
"29",
"31",
"33",
"34",
"35",
"37",
"38",
"39",
"41",
"43",
"44",
"46",
"47",
"49",
"51",
"52",
"53",
"55",
"57",
"58",
"59",
"61",
"62",
"65",
"66",
"67",
"68",
"69",
"71",
"73",
"76",
... | [
"nonn",
"new"
] | 8 | 1 | 1 | [
"A003415",
"A276085",
"A373842",
"A373847",
"A391927",
"A391938"
] | null | Antti Karttunen, Jan 15 2026 | 2026-01-15T19:27:33 | oeisdata/seq/A391/A391927.seq | 343aab5461c6102ee87dbfb94bf390a8 |
A391928 | Irregular table T(n, k) = (k*A002110(n-1)) mod prime(n), n >= 0, k = 0..prime(n)-1, read by rows, with row 0 = {0} by convention. | [
"0",
"0",
"1",
"0",
"2",
"1",
"0",
"1",
"2",
"3",
"4",
"0",
"2",
"4",
"6",
"1",
"3",
"5",
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"0",
"9",
"5",
"1",
"10",
"6",
"2",
"11",
"7",
"3",
"12",
"8",
"4",
"0",
"8",
"16"... | [
"nonn",
"tabf",
"look",
"new"
] | 19 | 0 | 5 | [
"A002110",
"A007504",
"A060735",
"A062347",
"A079276",
"A341805",
"A391928",
"A391929"
] | null | Antti Karttunen, Jan 04 2026 | 2026-01-06T10:05:17 | oeisdata/seq/A391/A391928.seq | 1f888ac4e99db90415f8c06e0fb86acd |
A391929 | Number of fixed points on row n of triangle A391930. | [
"1",
"2",
"2",
"10",
"10",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
"22",
... | [
"nonn",
"new"
] | 43 | 0 | 2 | [
"A002110",
"A079276",
"A341805",
"A343405",
"A360407",
"A391928",
"A391929",
"A391930"
] | null | Antti Karttunen, Jan 03 2026 | 2026-01-05T23:24:57 | oeisdata/seq/A391/A391929.seq | 20900402ae48f5182659259ac23c30d0 |
A391930 | Irregular triangle T(n, k) = Sum_{i=1..n} (k mod prime(i))*A002110(i-1), with n >= 0, and 0 <= k < A002110(n), read by rows. Here A002110(n) is the n-th primorial number. | [
"0",
"0",
"1",
"0",
"3",
"4",
"1",
"2",
"5",
"0",
"9",
"16",
"19",
"26",
"5",
"6",
"15",
"22",
"25",
"2",
"11",
"12",
"21",
"28",
"1",
"8",
"17",
"18",
"27",
"4",
"7",
"14",
"23",
"24",
"3",
"10",
"13",
"20",
"29",
"0",
"39",
"76",
... | [
"nonn",
"base",
"tabf",
"look",
"changed"
] | 40 | 0 | 5 | [
"A002110",
"A049345",
"A143293",
"A240673",
"A276085",
"A276086",
"A360407",
"A391929",
"A391930",
"A391931",
"A391933",
"A391934",
"A391935"
] | null | Antti Karttunen, Dec 29 2025 | 2026-01-05T23:24:18 | oeisdata/seq/A391/A391930.seq | 6645a8e31229fd06423beb7e04d0e31c |
A391931 | Irregular triangle T(n, k) = A143293(n-1) + Sum_{i=1..n} (k mod prime(i))*A002110(i-1), with n >= 1, and 1 <= k <= A002110(n), read by rows, where A002110 are the primorials and A143293 are their partial sums. | [
"2",
"1",
"6",
"7",
"4",
"5",
"8",
"3",
"18",
"25",
"28",
"35",
"14",
"15",
"24",
"31",
"34",
"11",
"20",
"21",
"30",
"37",
"10",
"17",
"26",
"27",
"36",
"13",
"16",
"23",
"32",
"33",
"12",
"19",
"22",
"29",
"38",
"9",
"78",
"115",
"148... | [
"nonn",
"tabf",
"less"
] | 17 | 1 | 1 | [
"A002110",
"A143293",
"A240673",
"A289234",
"A391930",
"A391931",
"A391932"
] | null | Antti Karttunen, Dec 29 2025 | 2025-12-31T22:20:48 | oeisdata/seq/A391/A391931.seq | 87ed882e2db1bb75f6c446fc33566d96 |
A391932 | Inverse permutation of A391931. | [
"2",
"1",
"8",
"5",
"6",
"3",
"4",
"7",
"38",
"23",
"18",
"33",
"28",
"13",
"14",
"29",
"24",
"9",
"34",
"19",
"20",
"35",
"30",
"15",
"10",
"25",
"26",
"11",
"36",
"21",
"16",
"31",
"32",
"17",
"12",
"27",
"22",
"37",
"248",
"143",
"10... | [
"nonn",
"tabf"
] | 9 | 1 | 1 | [
"A002110",
"A143293",
"A360407",
"A391931",
"A391932"
] | null | Antti Karttunen, Dec 30 2025 | 2025-12-30T23:40:27 | oeisdata/seq/A391/A391932.seq | 579ed62f7c8b02d5d1018f8f3f36fe42 |
A391933 | Irregular triangle T(n, k) = Product_{i=1..n} prime(i)^(k mod prime(i)), with n >= 0, and 0 <= k < A002110(n), read by rows. | [
"1",
"1",
"2",
"1",
"6",
"9",
"2",
"3",
"18",
"1",
"30",
"225",
"250",
"1875",
"18",
"5",
"150",
"1125",
"1250",
"3",
"90",
"25",
"750",
"5625",
"2",
"15",
"450",
"125",
"3750",
"9",
"10",
"75",
"2250",
"625",
"6",
"45",
"50",
"375",
"11250... | [
"nonn",
"tabf"
] | 25 | 0 | 3 | [
"A000012",
"A002110",
"A276086",
"A391930",
"A391933"
] | null | Antti Karttunen, Dec 29 2025 | 2025-12-31T22:20:41 | oeisdata/seq/A391/A391933.seq | 175885c8842d015676204521b3c79ef0 |
A391934 | Irregular triangle T(n, k) = Sum_{i=1..1+n} (A003415(k) mod prime(i))*A002110(i-1), with n >= 0, and 0 <= k < A002110(n), read by rows. | [
"0",
"0",
"0",
"0",
"0",
"9",
"9",
"26",
"9",
"0",
"0",
"39",
"39",
"146",
"39",
"155",
"39",
"162",
"186",
"15",
"39",
"68",
"39",
"85",
"52",
"136",
"39",
"7",
"39",
"114",
"92",
"201",
"39",
"88",
"92",
"31",
"193",
"136",
"39",
"0",
... | [
"nonn",
"tabf",
"new"
] | 13 | 0 | 6 | [
"A002110",
"A003415",
"A143293",
"A391930",
"A391934",
"A391935"
] | null | Antti Karttunen, Jan 05 2026 | 2026-01-05T16:55:22 | oeisdata/seq/A391/A391934.seq | 73a428edd2d6f3fcd887fcec01657824 |
A391935 | Irregular triangle T(n, k) = Sum_{i=1..1+n} (A276086(k) mod prime(i))*A002110(i-1), with n >= 0, and 0 <= k < A002110(n), read by rows. | [
"1",
"3",
"4",
"9",
"16",
"19",
"6",
"25",
"18",
"39",
"76",
"109",
"186",
"85",
"138",
"155",
"92",
"31",
"60",
"91",
"180",
"123",
"34",
"151",
"90",
"31",
"60",
"185",
"152",
"121",
"30",
"151",
"90",
"63",
"124",
"181",
"150",
"121",
"3... | [
"nonn",
"base",
"tabf",
"new"
] | 11 | 0 | 2 | [
"A002110",
"A143293",
"A276086",
"A391930",
"A391934",
"A391935"
] | null | Antti Karttunen, Jan 05 2026 | 2026-01-05T16:55:28 | oeisdata/seq/A391/A391935.seq | 18884a8c1476bfd11678268d140c3262 |
A391936 | a(n) = Sum_{i=1..A328404(n)} (A276086(n) mod prime(i))*A002110(i-1), where A276086 is the primorial base exp-function, and A328404(n) gives the length of A276086(n) in primorial base representation. | [
"1",
"4",
"1",
"6",
"25",
"18",
"5",
"2",
"1",
"60",
"91",
"180",
"3",
"34",
"151",
"90",
"1081",
"2160",
"185",
"1832",
"331",
"450",
"781",
"1350",
"1953",
"1594",
"1231",
"16110",
"21751",
"13260",
"15",
"28",
"7",
"12",
"19",
"6",
"5",
"2... | [
"nonn",
"base",
"new"
] | 13 | 0 | 2 | [
"A000035",
"A002110",
"A143293",
"A276086",
"A328404",
"A391930",
"A391935",
"A391936",
"A391937"
] | null | Antti Karttunen, Jan 06 2026 | 2026-01-06T11:11:20 | oeisdata/seq/A391/A391936.seq | 3e80dd0b01947146ab5d063a84b10ee8 |
A391937 | Numbers k such that A276086(k) = A391936(k). | [
"0",
"3",
"5",
"6",
"39",
"41",
"45",
"69",
"210",
"2316",
"30030",
"510555",
"510720",
"9699690",
"223092870"
] | [
"nonn",
"base",
"more",
"new"
] | 7 | 1 | 2 | [
"A002110",
"A048103",
"A276086",
"A343405",
"A391936",
"A391937"
] | null | Antti Karttunen, Jan 06 2026 | 2026-01-06T11:11:52 | oeisdata/seq/A391/A391937.seq | dc59a06ae1ae45f1e1fec6dc6be7e494 |
A391938 | Numbers k not divisible by p^p for any prime p, and for which A373842(k) >= k, where A373842 is the arithmetic derivative of the primorial base log-function. | [
"5",
"7",
"11",
"13",
"17",
"19",
"21",
"23",
"29",
"31",
"33",
"34",
"35",
"37",
"38",
"39",
"41",
"43",
"46",
"47",
"49",
"51",
"53",
"55",
"57",
"58",
"59",
"61",
"62",
"65",
"66",
"67",
"69",
"71",
"73",
"77",
"78",
"79",
"82",
"83",
... | [
"nonn",
"new"
] | 13 | 1 | 1 | [
"A003415",
"A048103",
"A276085",
"A276086",
"A351228",
"A373842",
"A373847",
"A373848",
"A391927",
"A391938",
"A391939"
] | null | Antti Karttunen, Jan 15 2026 | 2026-01-15T19:27:24 | oeisdata/seq/A391/A391938.seq | e1149ff9c89bba9ccd1611c76eedac1e |
A391939 | Composite numbers k such that A003415(k) <= A276086(k), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function. | [
"4",
"6",
"8",
"9",
"10",
"12",
"14",
"15",
"16",
"18",
"20",
"21",
"22",
"24",
"25",
"26",
"27",
"28",
"33",
"34",
"35",
"38",
"39",
"40",
"42",
"44",
"45",
"46",
"48",
"49",
"50",
"51",
"52",
"54",
"55",
"56",
"57",
"58",
"62",
"63",
... | [
"nonn",
"base",
"new"
] | 22 | 1 | 1 | [
"A002808",
"A003415",
"A276085",
"A276086",
"A276150",
"A351228",
"A373848",
"A391938",
"A391939"
] | null | Antti Karttunen, Jan 15 2026 | 2026-01-15T19:27:28 | oeisdata/seq/A391/A391939.seq | c4e68861b5a63d3a6beea44ecb0bca86 |
A391940 | RSA numbers. | [
"1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139",
"35794234179725868774991807832568455403003778024228226193532908190484670252364677411513516111204504060317568667",
"227010481295437363334259960947493668895875336466084780038173258247009162675779735389791151574... | [
"nonn",
"fini",
"full"
] | 15 | 1 | 1 | [
"A046388",
"A391940",
"A391941",
"A391942",
"A391943",
"A391944",
"A391945"
] | null | Antti Karttunen, Dec 28 2025 | 2025-12-28T22:25:34 | oeisdata/seq/A391/A391940.seq | 2159b1f7d6c44897118560b9f2dd7c5d |
A391941 | The smaller prime factor of RSA numbers. | [
"37975227936943673922808872755445627854565536638199",
"5846418214406154678836553182979162384198610505601062333",
"327414555693498015751146303749141488063642403240171463406883",
"3490529510847650949147849619903898133417764638493387843990820577",
"39685999459597454290161126162883786067576449112810064832555157... | [
"nonn",
"fini",
"hard",
"more"
] | 8 | 1 | 1 | [
"A020639",
"A391940",
"A391941",
"A391942"
] | null | Antti Karttunen, Dec 28 2025 | 2025-12-28T22:25:26 | oeisdata/seq/A391/A391941.seq | 79c5974a2ea98a01b1f6871db7f3f9e5 |
A391942 | The greater prime factor of RSA numbers. | [
"40094690950920881030683735292761468389214899724061",
"6122421090493547576937037317561418841225758554253106999",
"693342667110830181197325401899700641361965863127336680673013",
"32769132993266709549961988190834461413177642967992942539798288533",
"4553449864673597218840368689727440886435630126320506960099904... | [
"nonn",
"fini",
"hard",
"more"
] | 8 | 1 | 1 | [
"A006530",
"A391940",
"A391941",
"A391942"
] | null | Antti Karttunen, Dec 28 2025 | 2025-12-28T22:25:30 | oeisdata/seq/A391/A391942.seq | cb413161959ed87ed830b988d83ebf58 |
A391943 | Binary widths of RSA numbers. | [
"330",
"364",
"397",
"426",
"430",
"463",
"496",
"512",
"530",
"563",
"576",
"596",
"629",
"640",
"663",
"696",
"704",
"729",
"762",
"768",
"768",
"795",
"829",
"862",
"895",
"896",
"928",
"962",
"995",
"1024",
"1024",
"1028",
"1061",
"1094",
"1128... | [
"nonn",
"base",
"fini",
"full"
] | 7 | 1 | 1 | [
"A070939",
"A391940",
"A391943",
"A391944"
] | null | Antti Karttunen, Dec 28 2025 | 2025-12-28T22:12:55 | oeisdata/seq/A391/A391943.seq | a38c944537f805da5f4869d34caed60f |
A391944 | Number of decimal digits of RSA numbers. | [
"100",
"110",
"120",
"129",
"130",
"140",
"150",
"155",
"160",
"170",
"174",
"180",
"190",
"193",
"200",
"210",
"212",
"220",
"230",
"232",
"232",
"240",
"250",
"260",
"270",
"270",
"280",
"290",
"300",
"309",
"309",
"310",
"320",
"330",
"340",
"... | [
"nonn",
"base",
"fini",
"full"
] | 6 | 1 | 1 | [
"A055642",
"A391940",
"A391943",
"A391944",
"A391945"
] | null | Antti Karttunen, Dec 28 2025 | 2025-12-28T22:12:59 | oeisdata/seq/A391/A391944.seq | afd7a6992196b11c72b079cffd9261bb |
A391945 | Sum of decimal digits of RSA numbers. | [
"433",
"469",
"589",
"620",
"535",
"652",
"676",
"721",
"703",
"790",
"785",
"811",
"820",
"806",
"922",
"901",
"1009",
"973",
"1042",
"1006",
"1018",
"1099",
"1168",
"1102",
"1261",
"1222",
"1408",
"1306",
"1348",
"1381",
"1369",
"1420",
"1357",
"14... | [
"nonn",
"base",
"fini",
"full"
] | 8 | 1 | 1 | [
"A007953",
"A391940",
"A391944",
"A391945"
] | null | Antti Karttunen, Dec 28 2025 | 2025-12-28T22:13:08 | oeisdata/seq/A391/A391945.seq | 0fef5aff5e9e333f2aa5116493c9b0cb |
A391946 | a(n) = A276085(n) mod 2310, where A276085 is the primorial base log-function. | [
"0",
"1",
"2",
"2",
"6",
"3",
"30",
"3",
"4",
"7",
"210",
"4",
"0",
"31",
"8",
"4",
"0",
"5",
"0",
"8",
"32",
"211",
"0",
"5",
"12",
"1",
"6",
"32",
"0",
"9",
"0",
"5",
"212",
"1",
"36",
"6",
"0",
"1",
"2",
"9",
"0",
"33",
"0",
"2... | [
"nonn",
"new"
] | 12 | 1 | 3 | [
"A276085",
"A372576",
"A391864",
"A391946",
"A392598"
] | null | Antti Karttunen, Jan 17 2026 | 2026-01-18T15:40:38 | oeisdata/seq/A391/A391946.seq | 168276185e8c72b08cd359724a47d9e6 |
A391947 | Numbers k such that A003415(k) == A276085(k) (mod 2310) and A003415(k+1) == A276085(k+1) (mod 2310), where A003415 is the arithmetic derivative and A276085 is the primorial base log-function. . | [
"1",
"27717",
"41577",
"69297",
"131667",
"159387",
"235617",
"242547",
"270267",
"277197",
"332637",
"346497",
"519747",
"540537",
"595977",
"713787",
"803877",
"852387",
"928617",
"1025637",
"1178097",
"1205817",
"1212747",
"1247397",
"1288977",
"1316697",
"1344... | [
"nonn",
"new"
] | 13 | 1 | 2 | [
"A001221",
"A001222",
"A003415",
"A276085",
"A391864",
"A391947"
] | null | Antti Karttunen, Jan 17 2026 | 2026-01-18T15:40:43 | oeisdata/seq/A391/A391947.seq | eda8aa6bf17c6233199efb99a6350e9d |
A391948 | Primes p such that f(p) is prime and f(f(p)) = p, where f(k) = 10 * (10^(floor(log_10(k)) + 1) - 1)/9 - k. | [
"3",
"5",
"7",
"13",
"31",
"37",
"43",
"67",
"73",
"79",
"97",
"113",
"127",
"139",
"157",
"163",
"173",
"181",
"191",
"199",
"223",
"227",
"229",
"233",
"251",
"257",
"271",
"281",
"283",
"313",
"337",
"349",
"353",
"359",
"367",
"383",
"401",... | [
"nonn",
"base",
"changed"
] | 66 | 1 | 1 | [
"A068811",
"A105279",
"A391948"
] | null | Gavin A. Forrester, Dec 23 2025 | 2026-01-07T02:55:51 | oeisdata/seq/A391/A391948.seq | 91fe3ac92cf77016abd649fab249730c |
A391949 | Numbers k such that sigma(k) = psi(k) + phi(k) + omega(k)^6. | [
"48896",
"77844",
"384564",
"410484",
"505524",
"622164",
"682644",
"718932",
"747444",
"777684",
"783732",
"1046430",
"1220310",
"2014110",
"2558430",
"3639510",
"3642210",
"3828510",
"3881430",
"4093110",
"4130910",
"13649130",
"13806500",
"18027344",
"21758096",
... | [
"nonn",
"changed"
] | 11 | 1 | 1 | [
"A000010",
"A000203",
"A001221",
"A001615",
"A390049",
"A391312",
"A391749",
"A391763",
"A391908",
"A391949"
] | null | S. I. Dimitrov, Dec 23 2025 | 2026-01-05T03:58:34 | oeisdata/seq/A391/A391949.seq | 23b71123051ca0fda3d9bf76a5f1e827 |
A391950 | Triangle T(n,k) of coefficients of polynomials arising from Gaussian-weighted Chebyshev integrals. | [
"2",
"12",
"0",
"120",
"8",
"2",
"1680",
"160",
"48",
"0",
"30240",
"3360",
"1064",
"24",
"2",
"665280",
"80640",
"26208",
"960",
"108",
"0",
"17297280",
"2217600",
"731808",
"33696",
"4240",
"48",
"2",
"518918400",
"69189120",
"23063040",
"1216512",
"... | [
"nonn",
"tabl",
"changed"
] | 24 | 1 | 1 | [
"A370706",
"A391950"
] | null | Gabriele Celebre, Dec 23 2025 | 2026-01-08T22:04:27 | oeisdata/seq/A391/A391950.seq | 3b116824c6449651ab5ce108f069aae8 |
A391951 | Decimal expansion of the volume of an Escher's solid with unit shorter edge length. | [
"6",
"1",
"5",
"8",
"4",
"0",
"2",
"8",
"7",
"1",
"3",
"5",
"6",
"0",
"0",
"8",
"1",
"5",
"4",
"7",
"6",
"4",
"2",
"5",
"3",
"6",
"5",
"8",
"6",
"8",
"7",
"5",
"4",
"6",
"1",
"9",
"3",
"5",
"7",
"4",
"4",
"1",
"8",
"6",
"8",
"... | [
"nonn",
"cons",
"easy"
] | 10 | 1 | 1 | [
"A010482",
"A020784",
"A391653",
"A391951",
"A391952"
] | null | Paolo Xausa, Dec 23 2025 | 2025-12-25T09:37:45 | oeisdata/seq/A391/A391951.seq | a371ee5f7d59ababad1fdb7b1b1bea6c |
A391952 | Decimal expansion of the surface area of an Escher's solid with unit shorter edge length. | [
"2",
"2",
"6",
"2",
"7",
"4",
"1",
"6",
"9",
"9",
"7",
"9",
"6",
"9",
"5",
"2",
"0",
"7",
"8",
"0",
"8",
"2",
"7",
"0",
"1",
"9",
"5",
"8",
"7",
"3",
"5",
"5",
"1",
"6",
"9",
"2",
"5",
"7",
"1",
"1",
"4",
"7",
"5",
"0",
"0",
"... | [
"nonn",
"cons",
"easy"
] | 7 | 2 | 1 | [
"A002193",
"A391654",
"A391951",
"A391952"
] | null | Paolo Xausa, Dec 24 2025 | 2025-12-25T09:37:35 | oeisdata/seq/A391/A391952.seq | 2d29dbe4bb20635b2855c56d5b7600f4 |
A391953 | Decimal expansion of hypergeom([1/4, 1/2, 3/4], [2/3, 4/3], 1/27)/4. | [
"2",
"5",
"0",
"9",
"9",
"2",
"1",
"5",
"7",
"4",
"9",
"0",
"4",
"9",
"0",
"8",
"5",
"1",
"4",
"1",
"9",
"8",
"3",
"4",
"3",
"8",
"6",
"1",
"6",
"3",
"2",
"6",
"4",
"9",
"3",
"4",
"3",
"6",
"0",
"5",
"7",
"7",
"5",
"3",
"0",
"... | [
"nonn",
"cons"
] | 10 | 0 | 1 | [
"A019819",
"A094214",
"A130880",
"A192918",
"A382626",
"A382627",
"A391953"
] | null | Stefano Spezia, Dec 23 2025 | 2025-12-24T02:02:37 | oeisdata/seq/A391/A391953.seq | d2388a61ee84408bebddf6cefdaa415f |
A391955 | Number of pairs of Dyck paths of length 2*n touching the axis at the same points. | [
"1",
"1",
"2",
"7",
"38",
"274",
"2350",
"22531",
"233292",
"2555658",
"29232554",
"346013450",
"4211121946",
"52446977292",
"666024794758",
"8599676755883",
"112647192598844",
"1494224720878614",
"20041069061550880",
"271454315346852530",
"3709291397981162290",
"5108806605... | [
"nonn"
] | 15 | 0 | 3 | [
"A000108",
"A001181",
"A001246",
"A391955"
] | null | Ludovic Schwob, Dec 23 2025 | 2025-12-27T18:04:25 | oeisdata/seq/A391/A391955.seq | c5697246c610a04c7fbeacb33bb1fdfc |
A391956 | a(n) = 1/Product_{i = 1..n} w_i, where w_i is the i-th weight factor for Laguerre-Gauss quadrature of degree n. | [
"1",
"1",
"8",
"486",
"221184",
"750000000",
"18895680000000",
"3531604429335150000",
"4891710928142129430528000",
"50181356668275133180188221767680",
"3810801545415429046272000000000000000000",
"2141591602439723039788666936461886800000000000000",
"8904178923323813039189941618529553910755974... | [
"nonn"
] | 10 | 0 | 3 | [
"A387347",
"A391956",
"A391957"
] | null | A.H.M. Smeets, Dec 23 2025 | 2025-12-30T19:23:56 | oeisdata/seq/A391/A391956.seq | 06ec0d1ee09cbacf1eb418959697238e |
A391957 | Irregular triangle read by rows: exponents of the primes in the prime factorization of A391956(n) (primes in increasing order). | [
"3",
"1",
"5",
"13",
"3",
"7",
"1",
"9",
"12",
"10",
"7",
"4",
"6",
"5",
"13",
"41",
"2",
"3",
"11",
"27",
"32",
"1",
"9",
"32",
"24",
"18",
"7",
"16",
"16",
"14",
"5",
"21",
"46",
"31",
"10",
"3",
"19",
"26",
"21",
"6",
"1",
"17",
... | [
"nonn",
"tabf",
"changed"
] | 21 | 2 | 1 | [
"A000040",
"A000720",
"A391956",
"A391957"
] | null | A.H.M. Smeets, Dec 23 2025 | 2026-01-18T19:24:19 | oeisdata/seq/A391/A391957.seq | a0809bcd19f8c9cc4810818a7597131f |
A391958 | First column of A391957. | [
"0",
"0",
"3",
"1",
"13",
"7",
"12",
"4",
"41",
"27",
"32",
"16",
"46",
"26",
"33",
"11",
"113",
"83",
"88",
"56",
"102",
"66",
"73",
"35",
"138",
"94",
"101",
"55",
"119",
"69",
"78",
"26",
"289",
"227",
"232",
"168",
"246",
"178",
"185",
... | [
"nonn",
"new"
] | 50 | 0 | 3 | [
"A001511",
"A391956",
"A391957",
"A391958",
"A392083"
] | null | A.H.M. Smeets, Dec 23 2025 | 2026-01-13T13:40:39 | oeisdata/seq/A391/A391958.seq | da5c7193024b5464caa5105d6678a5dd |
A391959 | Second column of A391957. | [
"0",
"0",
"0",
"5",
"3",
"1",
"10",
"6",
"2",
"32",
"24",
"16",
"31",
"21",
"11",
"30",
"18",
"6",
"64",
"48",
"32",
"57",
"39",
"21",
"50",
"30",
"10",
"149",
"123",
"97",
"130",
"102",
"74",
"111",
"81",
"51",
"163",
"129",
"95",
"138",... | [
"nonn",
"new"
] | 32 | 0 | 4 | [
"A051064",
"A391956",
"A391957",
"A391959",
"A392084"
] | null | A.H.M. Smeets, Dec 28 2025 | 2026-01-13T13:40:27 | oeisdata/seq/A391/A391959.seq | 6c34f5978743ee088253e2348651dd26 |
A391960 | a(n) = Sum_{k=0..floor(n/3)} (k+1) * 2^k * 3^(n-3*k) * binomial(k,2*(n-3*k)). | [
"1",
"0",
"0",
"4",
"0",
"0",
"12",
"36",
"0",
"32",
"288",
"0",
"80",
"1440",
"720",
"192",
"5760",
"8640",
"448",
"20160",
"60480",
"13120",
"64512",
"322560",
"195840",
"193536",
"1451520",
"1746944",
"739584",
"5806080",
"11623424",
"5253120",
"212... | [
"nonn",
"easy"
] | 18 | 0 | 4 | [
"A390775",
"A390781",
"A391960",
"A391961"
] | null | Seiichi Manyama, Dec 23 2025 | 2025-12-29T18:54:19 | oeisdata/seq/A391/A391960.seq | 1c936d4ee8a0214ebea349deb3054384 |
A391961 | a(n) = Sum_{k=0..floor(n/3)} 2^k * 3^(n-3*k) * binomial(k+6,6) * binomial(k,2*(n-3*k)). | [
"1",
"0",
"0",
"14",
"0",
"0",
"112",
"336",
"0",
"672",
"6048",
"0",
"3360",
"60480",
"30240",
"14784",
"443520",
"665280",
"59136",
"2661120",
"7983360",
"1816320",
"13837824",
"69189120",
"42282240",
"64576512",
"484323840",
"583751168",
"339026688",
"290... | [
"nonn"
] | 14 | 0 | 4 | [
"A390775",
"A391723",
"A391960",
"A391961"
] | null | Seiichi Manyama, Dec 23 2025 | 2025-12-24T09:56:16 | oeisdata/seq/A391/A391961.seq | e5979ece577e59d276a41111dc019f10 |
A391962 | a(n) = Sum_{k=0..n} (k+1) * binomial(k,2*(n-k)). | [
"1",
"2",
"3",
"7",
"17",
"36",
"72",
"143",
"282",
"549",
"1057",
"2019",
"3832",
"7232",
"13581",
"25394",
"47303",
"87819",
"162549",
"300060",
"552552",
"1015259",
"1861674",
"3407433",
"6226053",
"11358407",
"20691504",
"37642816",
"68395609",
"12412720... | [
"nonn"
] | 19 | 0 | 2 | [
"A005251",
"A381421",
"A391962",
"A391963"
] | null | Seiichi Manyama, Dec 23 2025 | 2025-12-29T12:30:30 | oeisdata/seq/A391/A391962.seq | ddb4d9926982b279f2d8b1ea62f8477a |
A391963 | a(n) = Sum_{k=0..n} binomial(k+2,2) * binomial(k,2*(n-k)). | [
"1",
"3",
"6",
"16",
"45",
"111",
"253",
"561",
"1221",
"2603",
"5448",
"11238",
"22906",
"46206",
"92361",
"183151",
"360636",
"705672",
"1373067",
"2658129",
"5122275",
"9829497",
"18790449",
"35794569",
"67966000",
"128667132",
"242906916",
"457397132",
"85... | [
"nonn",
"easy"
] | 19 | 0 | 2 | [
"A005251",
"A382230",
"A391962",
"A391963"
] | null | Seiichi Manyama, Dec 23 2025 | 2025-12-29T18:54:36 | oeisdata/seq/A391/A391963.seq | da9679154c403dc1b3c24e384ae271f8 |
A391964 | a(n) = Sum_{k=0..n} (k+1) * 2^k * binomial(k,2*(n-k)). | [
"1",
"4",
"12",
"44",
"176",
"672",
"2448",
"8704",
"30528",
"105920",
"364032",
"1241088",
"4202752",
"14150656",
"47410176",
"158157824",
"525602816",
"1740840960",
"5748461568",
"18930761728",
"62190206976",
"203850235904",
"666838499328",
"2177331363840",
"7097215... | [
"nonn"
] | 16 | 0 | 2 | [
"A390700",
"A391964"
] | null | Seiichi Manyama, Dec 23 2025 | 2025-12-30T11:42:00 | oeisdata/seq/A391/A391964.seq | f526299a1e464cdbda15ca9ae0d06317 |
A391965 | a(n) = Sum_{k=0..n} 2^k * binomial(k+2,2) * binomial(k,2*(n-k)). | [
"1",
"6",
"24",
"104",
"480",
"2112",
"8752",
"34848",
"135168",
"513792",
"1920000",
"7071744",
"25728256",
"92622336",
"330405888",
"1169217536",
"4108296192",
"14344470528",
"49802211328",
"172027060224",
"591476293632",
"2025119416320",
"6907067105280",
"23474916556... | [
"nonn"
] | 17 | 0 | 2 | [
"A391875",
"A391965"
] | null | Seiichi Manyama, Dec 23 2025 | 2025-12-30T11:42:04 | oeisdata/seq/A391/A391965.seq | 0bd89bd3d4bca4e545fee2381c2de733 |
A391966 | Smallest integer k greater than 1 such that every solution of y^m = y (for all integers m > 1) in the commutative ring of n-adic integers is also a solution of y^k = y. | [
"3",
"3",
"3",
"5",
"3",
"7",
"3",
"3",
"5",
"11",
"3",
"13",
"7",
"5",
"3",
"17",
"3",
"19",
"5",
"7",
"11",
"23",
"3",
"5",
"13",
"3",
"7",
"29",
"5",
"31",
"3",
"11",
"17",
"13",
"3",
"37",
"19",
"13",
"5",
"41",
"7",
"43",
"11",... | [
"nonn",
"easy",
"new"
] | 26 | 2 | 1 | [
"A007947",
"A076566",
"A373387",
"A390598",
"A390915",
"A391966"
] | null | Marco Ripà, Dec 24 2025 | 2026-01-13T08:04:40 | oeisdata/seq/A391/A391966.seq | c6bd2c20dc198796f46065c9ee97078e |
A391967 | Numbers k such that sigma(k) + phi(k) = psi(k) + k. | [
"1",
"672",
"3120",
"7800",
"11904",
"23712",
"55552",
"195072",
"302784",
"492864",
"910336",
"1607808",
"1671072",
"1750656",
"6688560",
"13210368",
"15242496",
"16125952",
"16721400",
"17033984",
"17274624",
"26854656",
"56755968",
"633404992",
"805208064",
"8745... | [
"nonn"
] | 19 | 1 | 2 | [
"A000010",
"A000203",
"A001615",
"A391967"
] | null | Kaloian Ivanov, Dec 24 2025 | 2025-12-31T16:20:29 | oeisdata/seq/A391/A391967.seq | f69be171183b9537fac60d3e429de5b8 |
A391968 | Numbers divisible by at least 2 cubes greater than 1. | [
"216",
"432",
"648",
"864",
"1000",
"1080",
"1296",
"1512",
"1728",
"1944",
"2000",
"2160",
"2376",
"2592",
"2744",
"2808",
"3000",
"3024",
"3240",
"3375",
"3456",
"3672",
"3888",
"4000",
"4104",
"4320",
"4536",
"4752",
"4968",
"5000",
"5184",
"5400",
... | [
"nonn",
"easy",
"new"
] | 13 | 1 | 1 | [
"A002117",
"A004709",
"A013929",
"A024619",
"A046099",
"A052486",
"A126706",
"A286229",
"A286708",
"A332785",
"A372404",
"A372695",
"A375145",
"A376936",
"A378767",
"A383394",
"A388293",
"A388304",
"A388549",
"A391319",
"A391506",
"A391968"
] | null | Michael De Vlieger, Dec 24 2025 | 2026-01-06T11:11:07 | oeisdata/seq/A391/A391968.seq | a95aae525b493a65c549271183ebf517 |
A391969 | Number of quotients of the lattice of alternating sign matrices of size n isomorphic to the lattice of Dyck paths of length 2*n. | [
"1",
"1",
"2",
"6",
"28",
"202",
"2252",
"38756",
"1028964",
"42127054",
"2658809724",
"258630414936",
"38767099255644",
"8953246419943732",
"3185558965388036052",
"1745990974619361729172",
"1474075441986980210547940",
"1916876508718560362050901170",
"3839234705282352916635502966... | [
"nonn",
"changed"
] | 16 | 1 | 3 | [
"A000108",
"A005130",
"A390493",
"A391969",
"A391973"
] | null | Ludovic Schwob, Dec 24 2025 | 2026-01-11T21:38:29 | oeisdata/seq/A391/A391969.seq | aba8da24eee89610a7cb78edda849500 |
A391970 | Numbers m such that the product m*(m+1) has a set of prime divisors, from greatest down to 2, that is missing exactly two prime divisors. | [
"7",
"10",
"11",
"32",
"39",
"84",
"119",
"143",
"153",
"168",
"209",
"220",
"242",
"272",
"285",
"324",
"351",
"374",
"441",
"455",
"494",
"624",
"675",
"728",
"1224",
"1539",
"1700",
"2057",
"2184",
"2499",
"2600",
"3059",
"3135",
"4913",
"5082",... | [
"nonn"
] | 13 | 1 | 1 | [
"A391602",
"A391885",
"A391970"
] | null | Ken Clements, Dec 24 2025 | 2026-01-01T15:50:30 | oeisdata/seq/A391/A391970.seq | 6bb8a0675ba15fe94f47db4dcc1c33a5 |
A391971 | Triangle read by rows: T(n,k) = number of heapable permutations of length n with exactly k 321 patterns. | [
"1",
"1",
"1",
"2",
"5",
"14",
"3",
"42",
"18",
"11",
"132",
"82",
"84",
"27",
"22",
"11",
"1",
"429",
"339",
"456",
"256",
"243",
"143",
"124",
"61",
"43",
"28",
"4"
] | [
"nonn",
"tabf",
"more",
"new"
] | 20 | 1 | 4 | [
"A336282",
"A391697",
"A391776",
"A391777",
"A391971"
] | null | Manolopoulos Panagiotis, Dec 24 2025 | 2026-01-18T12:56:14 | oeisdata/seq/A391/A391971.seq | b08280cf137b06ac9f187a8771f915ff |
A391973 | Number of self-dual Catalan triangles of size 2*n+1. | [
"1",
"2",
"10",
"120",
"3434",
"233876",
"37866212"
] | [
"nonn",
"more"
] | 9 | 0 | 2 | [
"A390493",
"A391969",
"A391973"
] | null | Ludovic Schwob, Dec 25 2025 | 2025-12-30T11:39:21 | oeisdata/seq/A391/A391973.seq | 96394157fddff47a4d8f33326b1914eb |
A391975 | Number of irredundant sets in the n-triangular honeycomb bishop graph. | [
"2",
"5",
"19",
"94",
"559",
"3958",
"32957"
] | [
"nonn",
"more"
] | 4 | 1 | 1 | null | null | Eric W. Weisstein, Dec 25 2025 | 2025-12-25T09:37:05 | oeisdata/seq/A391/A391975.seq | 21930c68efd87fef39f608f1aaae507d |
A391976 | Number of irredundant sets in the n-triangular honeycomb obtuse knight graph. | [
"2",
"8",
"64",
"250",
"2256",
"25591"
] | [
"nonn",
"more"
] | 4 | 1 | 1 | null | null | Eric W. Weisstein, Dec 25 2025 | 2025-12-25T09:37:01 | oeisdata/seq/A391/A391976.seq | 04cf2edc88cf9bd91e8da9c5f6e405e0 |
A391978 | a(n) = 2*n*binomial(n, 4). | [
"0",
"0",
"0",
"8",
"50",
"180",
"490",
"1120",
"2268",
"4200",
"7260",
"11880",
"18590",
"28028",
"40950",
"58240",
"80920",
"110160",
"147288",
"193800",
"251370",
"321860",
"407330",
"510048",
"632500",
"777400",
"947700",
"1146600",
"1377558",
"1644300",... | [
"nonn",
"easy",
"new"
] | 15 | 1 | 4 | [
"A027764",
"A391978"
] | null | Eric W. Weisstein, Dec 25 2025 | 2026-01-08T03:04:19 | oeisdata/seq/A391/A391978.seq | f796916532e67bcd9de1998c381d89d3 |
A391979 | Number of closed "knight + wazir" tours on an 8 X n board. | [
"0",
"4",
"1484",
"290247",
"21767466",
"10808297353",
"2375931620966",
"460170137868876",
"86120998813237562",
"20912440756793175381",
"4269789533989878923996",
"903074393101632744082459",
"186843783417066650757163898",
"40434310805094436324334667019",
"8440630895242498970832101406644"
... | [
"nonn"
] | 11 | 1 | 2 | [
"A193055",
"A391979"
] | null | Don Knuth, Dec 25 2025 | 2025-12-25T19:45:39 | oeisdata/seq/A391/A391979.seq | abdceca28de0d63a693715b243ef122e |
A391980 | Achilles numbers divisible by at least 2 cubes greater than 1. | [
"432",
"648",
"864",
"1944",
"2000",
"2592",
"3456",
"3888",
"4000",
"5000",
"5400",
"5488",
"6912",
"9000",
"10125",
"10368",
"10584",
"10800",
"10976",
"13500",
"15552",
"16000",
"16200",
"16875",
"17496",
"18000",
"19208",
"20000",
"21168",
"21296",
"21... | [
"nonn",
"easy",
"new"
] | 11 | 1 | 1 | [
"A001694",
"A013929",
"A024619",
"A052486",
"A072102",
"A082020",
"A082695",
"A126706",
"A286708",
"A369632",
"A388293",
"A391968",
"A391980"
] | null | Michael De Vlieger, Dec 26 2025 | 2026-01-06T11:11:14 | oeisdata/seq/A391/A391980.seq | a295985872c432554f571f4bdf817318 |
A391981 | Irregular triangle read by rows where row n lists the trimmed zero-based partial alternating sums of the prime indices of n. | [
"1",
"2",
"1",
"0",
"3",
"1",
"1",
"4",
"1",
"0",
"1",
"2",
"0",
"1",
"2",
"5",
"1",
"0",
"2",
"6",
"1",
"3",
"2",
"1",
"1",
"0",
"1",
"0",
"7",
"1",
"1",
"1",
"8",
"1",
"0",
"3",
"2",
"2",
"1",
"4",
"9",
"1",
"0",
"1",
"1",
"... | [
"nonn",
"tabf",
"new"
] | 14 | 2 | 2 | [
"A000070",
"A000097",
"A000302",
"A001222",
"A028260",
"A055396",
"A056239",
"A061395",
"A103919",
"A112798",
"A124754",
"A209281",
"A239830",
"A247180",
"A283050",
"A316524",
"A344606",
"A344610",
"A344611",
"A344612",
"A344616",
"A345958",
"A346633",
"A346697",
"A34... | null | Gus Wiseman, Dec 26 2025 | 2026-01-11T17:53:45 | oeisdata/seq/A391/A391981.seq | 0d49d6da70da8a0fbd9e5f3041a375ec |
A391982 | Irregular triangle read by rows where row n lists the trimmed zero-based partial alternating sums of the reversed prime indices of n. | [
"1",
"2",
"1",
"0",
"3",
"2",
"-1",
"4",
"1",
"0",
"1",
"2",
"0",
"3",
"-2",
"5",
"2",
"-1",
"2",
"6",
"4",
"-3",
"3",
"-1",
"1",
"0",
"1",
"0",
"7",
"2",
"0",
"1",
"8",
"3",
"-2",
"3",
"4",
"-2",
"5",
"-4",
"9",
"2",
"-1",
"2",
... | [
"sign",
"tabf",
"new"
] | 7 | 2 | 2 | [
"A000070",
"A000097",
"A001222",
"A028260",
"A055396",
"A056239",
"A061395",
"A070003",
"A102750",
"A103919",
"A112798",
"A209281",
"A239830",
"A247180",
"A316524",
"A344606",
"A344610",
"A344611",
"A344612",
"A344616",
"A345958",
"A346633",
"A346697",
"A346699",
"A34... | null | Gus Wiseman, Jan 11 2026 | 2026-01-12T08:42:31 | oeisdata/seq/A391/A391982.seq | b8349ece7c42ed0c186fdc8a00ae0053 |
A391983 | Irregular triangle read by rows where row n lists the trimmed zero-based partial alternating sums of the n-th composition in standard order. | [
"1",
"2",
"1",
"0",
"3",
"2",
"-1",
"1",
"1",
"1",
"0",
"1",
"4",
"3",
"-2",
"2",
"0",
"2",
"-1",
"2",
"1",
"2",
"1",
"1",
"0",
"1",
"0",
"2",
"1",
"0",
"1",
"0",
"5",
"4",
"-3",
"3",
"-1",
"3",
"-2",
"3",
"2",
"1",
"2",
"0",
"1... | [
"sign",
"tabf",
"new"
] | 9 | 1 | 2 | [
"A000120",
"A003242",
"A005674",
"A011782",
"A025047",
"A065120",
"A066099",
"A070939",
"A116406",
"A124754",
"A124767",
"A209281",
"A316524",
"A342527",
"A344616",
"A344618",
"A344619",
"A346633",
"A346697",
"A346699",
"A357213",
"A390432",
"A390567",
"A390568",
"A39... | null | Gus Wiseman, Jan 10 2026 | 2026-01-11T17:54:03 | oeisdata/seq/A391/A391983.seq | 716c254584c182b2da36e7a0f57701a0 |
A391984 | Irregular triangle read by rows where row n lists the trimmed zero-based partial alternating sums of the reversed n-th composition in standard order. | [
"1",
"2",
"1",
"0",
"3",
"1",
"1",
"2",
"-1",
"1",
"0",
"1",
"4",
"1",
"2",
"2",
"0",
"1",
"0",
"2",
"3",
"-2",
"1",
"1",
"0",
"2",
"-1",
"2",
"1",
"0",
"1",
"0",
"5",
"1",
"3",
"2",
"1",
"1",
"0",
"3",
"3",
"-1",
"1",
"1",
"1",... | [
"sign",
"tabf",
"new"
] | 5 | 1 | 2 | [
"A000120",
"A001511",
"A003242",
"A005674",
"A011782",
"A025047",
"A065120",
"A066099",
"A070939",
"A116406",
"A124754",
"A124767",
"A209281",
"A316524",
"A342527",
"A344616",
"A344618",
"A344619",
"A346633",
"A346697",
"A346699",
"A357213",
"A390432",
"A390567",
"A39... | null | Gus Wiseman, Jan 11 2026 | 2026-01-12T08:42:27 | oeisdata/seq/A391/A391984.seq | 4044bf2d523b197a0c892f66d5b84d74 |
A391985 | a(n) = Sum_{k=0..floor(n/4)} (k+1) * 2^k * 3^(n-3*k) * binomial(n-2*k,k) * binomial(n-3*k,k). | [
"1",
"3",
"9",
"27",
"105",
"459",
"2025",
"8667",
"36369",
"151875",
"636417",
"2679075",
"11308761",
"47779227",
"201873465",
"852827211",
"3602606625",
"15218565363",
"64287833841",
"271557920115",
"1146975813225",
"4843839405771",
"20453167820457",
"86349979376667",... | [
"nonn"
] | 14 | 0 | 2 | [
"A098473",
"A098482",
"A390830",
"A391985",
"A391986"
] | null | Seiichi Manyama, Dec 26 2025 | 2025-12-31T14:26:08 | oeisdata/seq/A391/A391985.seq | cb22518790362e992c862959871363e3 |
A391986 | a(n) = Sum_{k=0..floor(n/4)} 2^k * 3^(n-3*k) * binomial(k+2,2) * binomial(n-2*k,k) * binomial(n-3*k,k). | [
"1",
"3",
"9",
"27",
"117",
"567",
"2673",
"11907",
"51597",
"222831",
"968841",
"4236219",
"18551781",
"81154791",
"354374433",
"1545091443",
"6729252957",
"29281369023",
"127304349273",
"552981937419",
"2399866971381",
"10405820054007",
"45080675201457",
"195138858704... | [
"nonn",
"changed"
] | 19 | 0 | 2 | [
"A098473",
"A098482",
"A390830",
"A391985",
"A391986"
] | null | Seiichi Manyama, Dec 26 2025 | 2026-01-05T15:15:17 | oeisdata/seq/A391/A391986.seq | 31ee5d6b3517347ea50a6df961c4797d |
A391987 | Decimal expansion of (7*sqrt(5)-5)/22. | [
"4",
"8",
"4",
"2",
"0",
"3",
"4",
"4",
"7",
"3",
"8",
"6",
"2",
"9",
"6",
"7",
"2",
"1",
"5",
"8",
"4",
"7",
"3",
"7",
"0",
"7",
"6",
"4",
"1",
"4",
"4",
"9",
"6",
"9",
"8",
"4",
"0",
"0",
"3",
"8",
"3",
"3",
"1",
"1",
"4",
"... | [
"nonn",
"cons"
] | 5 | 0 | 1 | [
"A000032",
"A001566",
"A001622",
"A189961",
"A391987"
] | null | Amiram Eldar, Dec 26 2025 | 2025-12-26T16:02:29 | oeisdata/seq/A391/A391987.seq | 62880086a227da31a2051b99781c7d22 |
A391988 | The number of exponential divisors of the exponentially squarefree numbers. | [
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"2",
"2",
"1",
"2",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"2",
"1",
"... | [
"nonn",
"easy"
] | 9 | 1 | 4 | [
"A049419",
"A074823",
"A209061",
"A262276",
"A278908",
"A388973",
"A391988",
"A391989"
] | null | Amiram Eldar, Dec 26 2025 | 2025-12-29T04:02:44 | oeisdata/seq/A391/A391988.seq | 3622853df3a47bae8de23ca2bc24d239 |
A391989 | The difference between the number of exponential divisors and the number of exponential unitary divisors for numbers that are not exponentially squarefree. | [
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"2",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"... | [
"nonn",
"easy"
] | 9 | 1 | 6 | [
"A000005",
"A001221",
"A049419",
"A130897",
"A174961",
"A262276",
"A278908",
"A322791",
"A361255",
"A391988",
"A391989"
] | null | Amiram Eldar, Dec 26 2025 | 2025-12-29T04:02:25 | oeisdata/seq/A391/A391989.seq | 5366befee08ab30ac734ad4de470ce61 |
A391990 | a(n) = Sum_{k=0..floor(n/2)} (k+1) * binomial(n,k) * binomial(n-k,k). | [
"1",
"1",
"5",
"13",
"43",
"131",
"411",
"1275",
"3963",
"12283",
"38023",
"117503",
"362605",
"1117429",
"3439229",
"10572957",
"32468787",
"99610515",
"305313711",
"935015271",
"2861204529",
"8749050009",
"26734768305",
"81642292977",
"249169635477",
"760033085301... | [
"nonn",
"changed"
] | 18 | 0 | 3 | [
"A002426",
"A098473",
"A391990"
] | null | Seiichi Manyama, Dec 26 2025 | 2026-01-05T15:15:31 | oeisdata/seq/A391/A391990.seq | 25ddc5424cbfa84342d20fda5bb249bb |
A391991 | Triangle read by rows: T(n,k) = number of digits in decimal representation of binomial(n,k), 0<=k<=n. | [
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"1",
"1",
"2",
"2",
"2",
"1",
"1",
"1",
"1",
"2",
"2",
"2",
"2",
"1",
"1",
"1",
"1",
"2",
"2",
"2",
"2",
"2",
"1",
"1",
"... | [
"nonn",
"tabl",
"easy",
"base"
] | 12 | 0 | 18 | [
"A007318",
"A055642",
"A101598",
"A391991",
"A391992"
] | null | Seiichi Manyama, Dec 26 2025 | 2025-12-26T08:32:02 | oeisdata/seq/A391/A391991.seq | 88f8b35f73fce2a54895b9f3530f6fdb |
A391992 | Number of digits in the decimal expansion of binomial(2*n,n). | [
"1",
"1",
"1",
"2",
"2",
"3",
"3",
"4",
"5",
"5",
"6",
"6",
"7",
"8",
"8",
"9",
"9",
"10",
"10",
"11",
"12",
"12",
"13",
"13",
"14",
"15",
"15",
"16",
"16",
"17",
"18",
"18",
"19",
"19",
"20",
"21",
"21",
"22",
"22",
"23",
"24",
"24",... | [
"nonn",
"easy",
"base",
"changed"
] | 17 | 0 | 4 | [
"A000984",
"A055642",
"A391991",
"A391992"
] | null | Seiichi Manyama, Dec 26 2025 | 2026-01-05T15:15:02 | oeisdata/seq/A391/A391992.seq | f8f27e35abdb3650d99a3bce537eae6b |
A391993 | Expansion of (2*x*(x - 7))/(x - 1)^3. | [
"0",
"14",
"40",
"78",
"128",
"190",
"264",
"350",
"448",
"558",
"680",
"814",
"960",
"1118",
"1288",
"1470",
"1664",
"1870",
"2088",
"2318",
"2560",
"2814",
"3080",
"3358",
"3648",
"3950",
"4264",
"4590",
"4928",
"5278",
"5640",
"6014",
"6400",
"679... | [
"nonn",
"easy",
"new"
] | 15 | 0 | 2 | [
"A391993",
"A392248"
] | null | Peter Luschny, Jan 09 2026 | 2026-01-10T19:16:04 | oeisdata/seq/A391/A391993.seq | e3b0174bafe45e2195690b2ae58dd906 |
A391994 | Expansion of (x^2*(3*x - 1))/((x - 1)^4*(x + 1)). | [
"0",
"0",
"-1",
"0",
"2",
"8",
"17",
"32",
"52",
"80",
"115",
"160",
"214",
"280",
"357",
"448",
"552",
"672",
"807",
"960",
"1130",
"1320",
"1529",
"1760",
"2012",
"2288",
"2587",
"2912",
"3262",
"3640",
"4045",
"4480",
"4944",
"5440",
"5967",
"... | [
"sign",
"easy",
"new"
] | 12 | 0 | 5 | [
"A002620",
"A391994",
"A392248"
] | null | Peter Luschny, Jan 09 2026 | 2026-01-10T19:16:14 | oeisdata/seq/A391/A391994.seq | 4f3b35766d6ff1464160e3cd30c93fcf |
A391995 | a(n) = (4*n^3 - 18*n^2 - 4*n + 9*(1 - (-1)^n)) / 48. | [
"0",
"0",
"-1",
"-1",
"-1",
"1",
"4",
"10",
"18",
"30",
"45",
"65",
"89",
"119",
"154",
"196",
"244",
"300",
"363",
"435",
"515",
"605",
"704",
"814",
"934",
"1066",
"1209",
"1365",
"1533",
"1715",
"1910",
"2120",
"2344",
"2584",
"2839",
"3111",
... | [
"sign",
"easy",
"new"
] | 13 | 0 | 7 | [
"A212964",
"A391995",
"A392248"
] | null | Peter Luschny, Jan 09 2026 | 2026-01-10T07:21:20 | oeisdata/seq/A391/A391995.seq | 53d97a996acfce05472451311cd70281 |
A391996 | Table read by rows: T(n, k) = floor((k/2)^2)*n^2. | [
"0",
"0",
"0",
"0",
"0",
"4",
"0",
"0",
"9",
"18",
"0",
"0",
"16",
"32",
"64",
"0",
"0",
"25",
"50",
"100",
"150",
"0",
"0",
"36",
"72",
"144",
"216",
"324",
"0",
"0",
"49",
"98",
"196",
"294",
"441",
"588",
"0",
"0",
"64",
"128",
"256"... | [
"nonn",
"tabl",
"new"
] | 15 | 0 | 6 | [
"A212766",
"A391996",
"A391997"
] | null | Peter Luschny, Jan 10 2026 | 2026-01-11T05:09:16 | oeisdata/seq/A391/A391996.seq | ec151977717f46750027d6f77400e7da |
A391997 | a(n) = Sum_{k=0..n} floor((k/2)^2)*n^2. Row sums of A391996. | [
"0",
"0",
"4",
"27",
"112",
"325",
"792",
"1666",
"3200",
"5670",
"9500",
"15125",
"23184",
"34307",
"49392",
"69300",
"95232",
"128316",
"170100",
"222015",
"286000",
"363825",
"457864",
"570262",
"703872",
"861250",
"1045772",
"1260441",
"1509200",
"179553... | [
"nonn",
"new"
] | 10 | 0 | 3 | [
"A391997"
] | null | Peter Luschny, Jan 10 2026 | 2026-01-10T08:51:18 | oeisdata/seq/A391/A391997.seq | bc587496eaa567394b9ba1f27498cd59 |
A391998 | Composite numbers k such that k + 1 is not a power of an odd prime and 2*k + 1 is not a prime power. | [
"25",
"27",
"32",
"34",
"38",
"45",
"49",
"55",
"57",
"64",
"76",
"77",
"85",
"87",
"91",
"92",
"93",
"94",
"104",
"110",
"115",
"117",
"118",
"122",
"123",
"129",
"132",
"133",
"142",
"143",
"145",
"147",
"152",
"154",
"159",
"160",
"161",
"... | [
"nonn",
"changed"
] | 16 | 1 | 1 | [
"A093880",
"A391998",
"A392001"
] | null | Peter Luschny, Jan 01 2026 | 2026-01-07T21:17:30 | oeisdata/seq/A391/A391998.seq | 0b400a99d114c99f0e10263a226ada82 |
A391999 | Number of undirected closed knight's tours on a 9 X (2n) board. | [
"0",
"0",
"3374967940",
"7112881119092574"
] | [
"nonn",
"more"
] | 9 | 1 | 3 | [
"A000004",
"A001230",
"A169764",
"A175855",
"A175881",
"A193054",
"A193055",
"A391999",
"A392000",
"X2"
] | null | Peter Luschny, Dec 27 2025 | 2025-12-27T13:06:04 | oeisdata/seq/A391/A391999.seq | b793ca4399fc443e491b09f8aff66613 |
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