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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
A002101 | Nearest integer to 4 * Pi * n^3 / 3. | [
"0",
"4",
"34",
"113",
"268",
"524",
"905",
"1437",
"2145",
"3054",
"4189",
"5575",
"7238",
"9203",
"11494",
"14137",
"17157",
"20580",
"24429",
"28731",
"33510",
"38792",
"44602",
"50965",
"57906",
"65450",
"73622",
"82448",
"91952",
"102160",
"113097",
... | [
"nonn",
"easy"
] | 23 | 0 | 2 | null | [
"M3653",
"N1486"
] | N. J. A. Sloane | 2021-12-23T22:44:56 | oeisdata/seq/A002/A002101.seq | 41ce8e6864fba418627e4baaa9cf37ac |
A002102 | Number of nonnegative solutions to x^2 + y^2 + z^2 = n. | [
"1",
"3",
"3",
"1",
"3",
"6",
"3",
"0",
"3",
"6",
"6",
"3",
"1",
"6",
"6",
"0",
"3",
"9",
"6",
"3",
"6",
"6",
"3",
"0",
"3",
"9",
"12",
"4",
"0",
"12",
"6",
"0",
"3",
"6",
"9",
"6",
"6",
"6",
"9",
"0",
"6",
"15",
"6",
"3",
"3",
... | [
"nonn"
] | 23 | 0 | 2 | [
"A000606",
"A002102"
] | [
"M2265",
"N0895"
] | N. J. A. Sloane | 2023-10-14T23:45:13 | oeisdata/seq/A002/A002102.seq | 0751af4bc370510750a218d9761385e2 |
A002103 | Coefficients of expansion of Jacobi nome q in certain powers of (1/2)*(1 - sqrt(k')) / (1 + sqrt(k')). | [
"1",
"2",
"15",
"150",
"1707",
"20910",
"268616",
"3567400",
"48555069",
"673458874",
"9481557398",
"135119529972",
"1944997539623",
"28235172753886",
"412850231439153",
"6074299605748746",
"89857589279037102",
"1335623521633805028"
] | [
"nonn",
"easy",
"nice"
] | 69 | 0 | 2 | [
"A001936",
"A002103",
"A002639",
"A079006"
] | [
"M2082",
"N0823"
] | N. J. A. Sloane | 2019-12-24T00:50:19 | oeisdata/seq/A002/A002103.seq | a3ca6e301c7f0029ef4b5a9bdc7f4912 |
A002104 | Logarithmic numbers. | [
"0",
"1",
"3",
"8",
"24",
"89",
"415",
"2372",
"16072",
"125673",
"1112083",
"10976184",
"119481296",
"1421542641",
"18348340127",
"255323504932",
"3809950977008",
"60683990530225",
"1027542662934915",
"18430998766219336",
"349096664728623336",
"6962409983976703337",
"145... | [
"nonn",
"easy",
"nice"
] | 121 | 0 | 3 | [
"A001338",
"A002104",
"A006231",
"A007526",
"A030297",
"A133942"
] | [
"M2749",
"N1105"
] | N. J. A. Sloane | 2024-07-20T10:54:29 | oeisdata/seq/A002/A002104.seq | 81b09a99a7700d9d1ffd4b22af189f54 |
A002105 | Reduced tangent numbers: 2^n*(2^{2n} - 1)*|B_{2n}|/n, where B_n = Bernoulli numbers. | [
"1",
"1",
"4",
"34",
"496",
"11056",
"349504",
"14873104",
"819786496",
"56814228736",
"4835447317504",
"495812444583424",
"60283564499562496",
"8575634961418940416",
"1411083019275488149504",
"265929039218907754399744",
"56906245479134057176170496",
"13722623393637762299131396096"... | [
"easy",
"nonn",
"nice"
] | 236 | 1 | 3 | [
"A000111",
"A000217",
"A000364",
"A000464",
"A002105",
"A002439",
"A008281",
"A008301",
"A079144",
"A158690",
"A210108"
] | [
"M3655",
"N1487"
] | N. J. A. Sloane | 2025-11-11T15:52:46 | oeisdata/seq/A002/A002105.seq | 64f74eaeeb6371a72d24cd85f84116e8 |
A002106 | Number of transitive permutation groups of degree n. | [
"1",
"1",
"2",
"5",
"5",
"16",
"7",
"50",
"34",
"45",
"8",
"301",
"9",
"63",
"104",
"1954",
"10",
"983",
"8",
"1117",
"164",
"59",
"7",
"25000",
"211",
"96",
"2392",
"1854",
"8",
"5712",
"12",
"2801324",
"162",
"115",
"407",
"121279",
"11",
"... | [
"nonn",
"core",
"hard",
"more",
"nice"
] | 98 | 1 | 3 | [
"A000001",
"A000019",
"A002106",
"A177244",
"A186277"
] | [
"M1316",
"N0504"
] | N. J. A. Sloane | 2025-05-27T10:34:57 | oeisdata/seq/A002/A002106.seq | d1cb8403ae257fc81fdc0d0fd178500a |
A002107 | Expansion of Product_{k>=1} (1 - x^k)^2. | [
"1",
"-2",
"-1",
"2",
"1",
"2",
"-2",
"0",
"-2",
"-2",
"1",
"0",
"0",
"2",
"3",
"-2",
"2",
"0",
"0",
"-2",
"-2",
"0",
"0",
"-2",
"-1",
"0",
"2",
"2",
"-2",
"2",
"1",
"2",
"0",
"2",
"-2",
"-2",
"2",
"0",
"-2",
"0",
"-4",
"0",
"0",
... | [
"sign",
"nice"
] | 130 | 0 | 2 | [
"A000594",
"A000712",
"A000727",
"A000731",
"A000735",
"A000739",
"A002107",
"A010815",
"A010816",
"A010840",
"A258406"
] | [
"M0091",
"N0028"
] | N. J. A. Sloane | 2025-11-10T21:50:37 | oeisdata/seq/A002/A002107.seq | 97b9748cc2331bb985fa13009511333c |
A002108 | 4th powers written backwards. | [
"1",
"61",
"18",
"652",
"526",
"6921",
"1042",
"6904",
"1656",
"1",
"14641",
"63702",
"16582",
"61483",
"52605",
"63556",
"12538",
"679401",
"123031",
"61",
"184491",
"652432",
"148972",
"677133",
"526093",
"679654",
"144135",
"656416",
"182707",
"18",
"12... | [
"nonn",
"base"
] | 26 | 1 | 2 | [
"A000583",
"A002108",
"A002942",
"A004086",
"A004165",
"A186080"
] | null | N. J. A. Sloane | 2023-10-14T22:32:45 | oeisdata/seq/A002/A002108.seq | 46dc793f09b96a83870b42bdb7e9a79a |
A002109 | Hyperfactorials: Product_{k = 1..n} k^k. | [
"1",
"1",
"4",
"108",
"27648",
"86400000",
"4031078400000",
"3319766398771200000",
"55696437941726556979200000",
"21577941222941856209168026828800000",
"215779412229418562091680268288000000000000000",
"61564384586635053951550731889313964883968000000000000000"
] | [
"nonn",
"easy",
"nice"
] | 196 | 0 | 3 | [
"A000142",
"A000178",
"A000312",
"A001358",
"A001923",
"A002109",
"A002981",
"A002982",
"A005234",
"A006794",
"A014545",
"A018239",
"A051675",
"A054374",
"A057704",
"A057705",
"A074962",
"A100015",
"A240993",
"A246839",
"A255321",
"A255323",
"A255344",
"A261175",
"A34... | [
"M3706",
"N1514"
] | N. J. A. Sloane | 2025-11-05T15:35:24 | oeisdata/seq/A002/A002109.seq | e9e6713801cc71a8115a6b6da5b181ce |
A002110 | Primorial numbers (first definition): product of first n primes. Sometimes written prime(n)#. | [
"1",
"2",
"6",
"30",
"210",
"2310",
"30030",
"510510",
"9699690",
"223092870",
"6469693230",
"200560490130",
"7420738134810",
"304250263527210",
"13082761331670030",
"614889782588491410",
"32589158477190044730",
"1922760350154212639070",
"117288381359406970983270",
"78583215510... | [
"nonn",
"easy",
"nice",
"core"
] | 392 | 0 | 2 | [
"A001008",
"A001615",
"A002110",
"A002182",
"A002201",
"A002805",
"A003418",
"A005117",
"A005235",
"A006862",
"A024451",
"A033188",
"A034386",
"A034387",
"A034444",
"A034448",
"A035345",
"A035346",
"A036691",
"A049345",
"A053589",
"A057588",
"A060735",
"A061720",
"A06... | [
"M1691",
"N0668"
] | N. J. A. Sloane and J. H. Conway | 2025-11-05T15:35:24 | oeisdata/seq/A002/A002110.seq | 6b10286d55ad67368c11651998e34075 |
A002111 | Glaisher's G numbers. | [
"1",
"5",
"49",
"809",
"20317",
"722813",
"34607305",
"2145998417",
"167317266613",
"16020403322021",
"1848020950359841",
"252778977216700025",
"40453941942593304589",
"7488583061542051450829",
"1587688770629724715374457",
"382218817191632327375004833",
"10369117560649061728877809904... | [
"nonn",
"nice",
"easy"
] | 103 | 1 | 2 | [
"A002111",
"A033470",
"A083007"
] | [
"M4007",
"N1660"
] | N. J. A. Sloane | 2025-11-24T15:59:05 | oeisdata/seq/A002/A002111.seq | e9ae5b3356a8952c817da65c50748511 |
A002112 | Glaisher's H numbers. | [
"3",
"33",
"903",
"46113",
"3784503",
"455538993",
"75603118503",
"16546026500673",
"4616979073434903",
"1599868423237443153",
"674014138103352845703",
"339274210193051498798433",
"201097637653063767131142903",
"138634566390566081044811718513"
] | [
"nonn",
"nice",
"easy"
] | 53 | 1 | 1 | null | [
"M3135",
"N1272"
] | N. J. A. Sloane | 2021-12-24T02:31:10 | oeisdata/seq/A002/A002112.seq | 880c8efafeeef4d0c1a9b0ab132cfc96 |
A002113 | Palindromes in base 10. | [
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"11",
"22",
"33",
"44",
"55",
"66",
"77",
"88",
"99",
"101",
"111",
"121",
"131",
"141",
"151",
"161",
"171",
"181",
"191",
"202",
"212",
"222",
"232",
"242",
"252",
"262",
"272",
"282",
"29... | [
"nonn",
"base",
"easy",
"nice",
"core"
] | 389 | 1 | 3 | [
"A002113",
"A002385",
"A004086",
"A006995",
"A014190",
"A014192",
"A029742",
"A029803",
"A029952",
"A029953",
"A029954",
"A029955",
"A029956",
"A032350",
"A056524",
"A056525",
"A057148",
"A061917",
"A064834",
"A086862",
"A088601",
"A110745",
"A118031",
"A118594",
"A11... | [
"M0484",
"N0178"
] | N. J. A. Sloane | 2025-11-05T15:21:41 | oeisdata/seq/A002/A002113.seq | a8cad3a087be2e762c7c62c2683f94ef |
A002114 | Glaisher's H' numbers. | [
"1",
"11",
"301",
"15371",
"1261501",
"151846331",
"25201039501",
"5515342166891",
"1538993024478301",
"533289474412481051",
"224671379367784281901",
"113091403397683832932811",
"67032545884354589043714301",
"46211522130188693681603906171"
] | [
"nice",
"easy",
"nonn"
] | 71 | 1 | 2 | null | [
"M4810",
"N2057"
] | N. J. A. Sloane | 2025-11-05T15:21:41 | oeisdata/seq/A002/A002114.seq | 78c36b72ba94c521f00a452235adb72a |
A002115 | Generalized Euler numbers. | [
"1",
"1",
"19",
"1513",
"315523",
"136085041",
"105261234643",
"132705221399353",
"254604707462013571",
"705927677520644167681",
"2716778010767155313771539",
"14050650308943101316593590153",
"95096065132610734223282520762883",
"823813936407337360148622860507620561"
] | [
"nonn"
] | 58 | 0 | 3 | [
"A000364",
"A002115",
"A178963",
"A278073"
] | [
"M5082",
"N2199"
] | N. J. A. Sloane | 2025-01-15T04:16:43 | oeisdata/seq/A002/A002115.seq | 5946b08fa3ef42d52f3ce109987953a1 |
A002116 | Some special numbers. | [
"2",
"20",
"402",
"14440",
"825502",
"69055260",
"7960285802",
"1209873973712"
] | [
"nonn",
"more"
] | 11 | 0 | 1 | null | [
"M2125",
"N0842"
] | N. J. A. Sloane | 2023-10-14T22:33:14 | oeisdata/seq/A002/A002116.seq | 4d3a4510bfe87ba4c9715958837f4e25 |
A002117 | Apéry's number or Apéry's constant zeta(3). Decimal expansion of zeta(3) = Sum_{m >= 1} 1/m^3. | [
"1",
"2",
"0",
"2",
"0",
"5",
"6",
"9",
"0",
"3",
"1",
"5",
"9",
"5",
"9",
"4",
"2",
"8",
"5",
"3",
"9",
"9",
"7",
"3",
"8",
"1",
"6",
"1",
"5",
"1",
"1",
"4",
"4",
"9",
"9",
"9",
"0",
"7",
"6",
"4",
"9",
"8",
"6",
"2",
"9",
"... | [
"cons",
"nonn",
"nice"
] | 487 | 1 | 2 | [
"A000578",
"A001008",
"A002117",
"A002805",
"A013631",
"A013661",
"A013663",
"A013667",
"A013669",
"A013671",
"A013675",
"A013677",
"A013679",
"A059956",
"A084225",
"A084226",
"A143003",
"A143007",
"A152623",
"A175577",
"A175578",
"A197070",
"A233090",
"A233091",
"A29... | [
"M0020"
] | N. J. A. Sloane | 2025-11-12T16:59:56 | oeisdata/seq/A002/A002117.seq | b76d6f7d556e1ecd3bdd9f2a647b475e |
A002118 | 5th powers written backwards. | [
"0",
"1",
"23",
"342",
"4201",
"5213",
"6777",
"70861",
"86723",
"94095",
"1",
"150161",
"238842",
"392173",
"428735",
"573957",
"6758401",
"7589141",
"8659881",
"9906742",
"23",
"1014804",
"2363515",
"3436346",
"4262697",
"5265679",
"67318811",
"70984341",
"8... | [
"nonn",
"base"
] | 8 | 0 | 3 | null | null | N. J. A. Sloane | 2023-10-14T22:33:34 | oeisdata/seq/A002/A002118.seq | 418cff32cdf219ea2a087ae8da0b1ea3 |
A002119 | Bessel polynomial y_n(-2). | [
"1",
"-1",
"7",
"-71",
"1001",
"-18089",
"398959",
"-10391023",
"312129649",
"-10622799089",
"403978495031",
"-16977719590391",
"781379079653017",
"-39085931702241241",
"2111421691000680031",
"-122501544009741683039",
"7597207150294985028449",
"-501538173463478753560673"
] | [
"sign",
"easy",
"nice"
] | 105 | 0 | 3 | [
"A000806",
"A001498",
"A001514",
"A001517",
"A002119",
"A006199",
"A033815",
"A053556",
"A053557",
"A065707",
"A065920",
"A065921",
"A065922",
"A065923"
] | [
"M4444",
"N1880"
] | N. J. A. Sloane | 2025-11-05T15:35:24 | oeisdata/seq/A002/A002119.seq | de2ffcf07cc740981bbc0990d73d6930 |
A002120 | a(1) = 0, a(2) = -2; for n > 2, a(n) + a(n-2) - a(n-3) - a(n-5) - ... - a(n-p) = (-1)^(n+1)*n if n is prime, otherwise = 0, where p = largest prime < n. | [
"0",
"-2",
"3",
"2",
"0",
"1",
"7",
"2",
"-6",
"8",
"22",
"-7",
"0",
"33",
"3",
"-14",
"51",
"46",
"-19",
"12",
"94",
"42",
"-23",
"113",
"150",
"-54",
"48",
"345",
"116",
"-109",
"403",
"498",
"-140",
"219",
"1057",
"326",
"-259",
"1271",
... | [
"sign"
] | 17 | 1 | 2 | null | [
"M0414",
"N0158"
] | N. J. A. Sloane | 2023-10-14T22:34:34 | oeisdata/seq/A002/A002120.seq | 19d6fd60a0e91ad8ddb0a0e9720ae500 |
A002121 | a(0) = 1, a(1) = 0, a(2) = -1; for n >= 3, a(n) = - a(n-2) + Sum_{ primes p with 3 <= p <= n} a(n-p). | [
"1",
"0",
"-1",
"1",
"1",
"-1",
"0",
"2",
"0",
"-2",
"2",
"4",
"-3",
"-2",
"8",
"1",
"-8",
"8",
"12",
"-11",
"-4",
"25",
"4",
"-24",
"21",
"40",
"-31",
"-16",
"82",
"14",
"-81",
"71",
"131",
"-99",
"-48",
"258",
"46",
"-249",
"223",
"422"... | [
"sign",
"easy",
"look"
] | 26 | 0 | 8 | [
"A002100",
"A002121",
"A002125",
"A065091"
] | [
"M0023",
"N0005"
] | N. J. A. Sloane | 2023-10-14T22:35:18 | oeisdata/seq/A002/A002121.seq | 2b0ebc36a9e01b6823c0711cba2eaa66 |
A002122 | a(n) = Sum_{t=0..n} g(t)*g(n-t) where g(t) = A002121(t). | [
"1",
"0",
"-2",
"2",
"3",
"-4",
"-1",
"8",
"-1",
"-10",
"9",
"16",
"-18",
"-12",
"42",
"4",
"-58",
"40",
"82",
"-88",
"-54",
"188",
"18",
"-248",
"151",
"354",
"-338",
"-260",
"760",
"120",
"-1031",
"574",
"1460",
"-1324",
"-1076",
"2948",
"542... | [
"sign"
] | 25 | 0 | 3 | [
"A002121",
"A002122"
] | [
"M0273",
"N0096"
] | N. J. A. Sloane | 2023-10-14T22:35:57 | oeisdata/seq/A002/A002122.seq | 53f3714cceb4359f2534935954dd7b2b |
A002123 | a(1) = 0, a(2) = 0; for n > 2, a(n) - a(n-3) - a(n-5) - ... - a(n-p) = n if n is prime, otherwise = 0, where p = largest prime < n. | [
"0",
"0",
"3",
"0",
"5",
"-3",
"7",
"-8",
"3",
"-15",
"22",
"-15",
"39",
"-35",
"38",
"-72",
"85",
"-111",
"152",
"-175",
"241",
"-308",
"414",
"-551",
"655",
"-897",
"1164",
"-1463",
"2001",
"-2538",
"3286",
"-4296",
"5503",
"-7259",
"9357",
"-1... | [
"sign"
] | 17 | 1 | 3 | [
"A002123",
"A061397",
"A065091"
] | [
"M2198",
"N0876"
] | N. J. A. Sloane | 2016-12-26T02:01:46 | oeisdata/seq/A002/A002123.seq | 939911b0e757f0012bec4a7463b747f7 |
A002124 | Number of compositions of n into a sum of odd primes. | [
"1",
"0",
"0",
"1",
"0",
"1",
"1",
"1",
"2",
"1",
"3",
"4",
"3",
"7",
"7",
"8",
"14",
"15",
"21",
"28",
"33",
"47",
"58",
"76",
"103",
"125",
"169",
"220",
"277",
"373",
"476",
"616",
"810",
"1037",
"1361",
"1763",
"2279",
"2984",
"3846",
... | [
"nonn"
] | 47 | 0 | 9 | [
"A002124",
"A002125",
"A023360",
"A024939",
"A065091",
"A077608"
] | [
"M0154",
"N0062"
] | N. J. A. Sloane | 2022-04-13T13:25:16 | oeisdata/seq/A002/A002124.seq | 301f8ed4d7a42bd94c90d8f9984d5fa9 |
A002125 | a(n) = Sum_{k=0..n} f(k)*f(n-k) where f(k) = A002124(k). | [
"1",
"0",
"0",
"2",
"0",
"2",
"3",
"2",
"6",
"4",
"9",
"14",
"11",
"26",
"29",
"34",
"62",
"68",
"99",
"140",
"169",
"252",
"322",
"430",
"607",
"764",
"1059",
"1424",
"1845",
"2546",
"3344",
"4442",
"6002",
"7876",
"10575",
"14058",
"18575",
... | [
"nonn"
] | 25 | 0 | 4 | null | [
"M0024",
"N0006"
] | N. J. A. Sloane | 2023-10-14T22:36:36 | oeisdata/seq/A002/A002125.seq | e6d5166b4cebcb17ebb8a167876bcefe |
A002126 | Number of solutions to n=p+q where p and q are primes or zero. | [
"1",
"0",
"2",
"2",
"1",
"4",
"1",
"4",
"2",
"2",
"3",
"2",
"2",
"4",
"3",
"2",
"4",
"2",
"4",
"4",
"4",
"2",
"5",
"2",
"6",
"2",
"5",
"0",
"4",
"2",
"6",
"4",
"4",
"2",
"7",
"0",
"8",
"2",
"3",
"2",
"6",
"2",
"8",
"4",
"6",
"... | [
"nonn"
] | 25 | 0 | 3 | [
"A002126",
"A002375",
"A045917",
"A061358",
"A073610"
] | [
"M0202",
"N0075"
] | N. J. A. Sloane | 2020-03-09T20:19:12 | oeisdata/seq/A002/A002126.seq | a66570f9aad79809f2ca5ca76abbe5e1 |
A002127 | MacMahon's generalized sum of divisors function. | [
"1",
"3",
"9",
"15",
"30",
"45",
"67",
"99",
"135",
"175",
"231",
"306",
"354",
"465",
"540",
"681",
"765",
"945",
"1040",
"1305",
"1386",
"1695",
"1779",
"2205",
"2290",
"2754",
"2835",
"3438",
"3480",
"4185",
"4272",
"5076",
"5004",
"6100",
"5985... | [
"nonn",
"easy"
] | 54 | 3 | 2 | [
"A002127",
"A002128",
"A060043",
"A385001"
] | [
"M2770",
"N1114"
] | N. J. A. Sloane | 2026-01-03T02:50:42 | oeisdata/seq/A002/A002127.seq | 3a555bca890d0c6c24ab8258aafb4e6e |
A002128 | MacMahon's generalized sum of divisors function. | [
"1",
"3",
"9",
"22",
"42",
"81",
"140",
"231",
"351",
"551",
"783",
"1134",
"1546",
"2142",
"2835",
"3758",
"4818",
"6237",
"7826",
"9885",
"12159",
"14974",
"18261",
"22113",
"26511",
"31668",
"37611",
"44149",
"52074",
"60660",
"70569",
"81396",
"943... | [
"nonn",
"easy"
] | 36 | 6 | 2 | [
"A002127",
"A002128",
"A060043",
"A385001"
] | [
"M2784",
"N1119"
] | N. J. A. Sloane | 2025-11-05T15:21:41 | oeisdata/seq/A002/A002128.seq | 9869fb0c87c6fe81bba2c1214f0c0434 |
A002129 | Generalized sum of divisors function: excess of sum of odd divisors of n over sum of even divisors of n. | [
"1",
"-1",
"4",
"-5",
"6",
"-4",
"8",
"-13",
"13",
"-6",
"12",
"-20",
"14",
"-8",
"24",
"-29",
"18",
"-13",
"20",
"-30",
"32",
"-12",
"24",
"-52",
"31",
"-14",
"40",
"-40",
"30",
"-24",
"32",
"-61",
"48",
"-18",
"48",
"-65",
"38",
"-20",
"5... | [
"sign",
"easy",
"nice",
"mult"
] | 76 | 1 | 3 | [
"A002129",
"A003462",
"A010054",
"A024919",
"A036563",
"A060044",
"A113184"
] | [
"M3236",
"N1307"
] | N. J. A. Sloane | 2025-11-05T15:21:41 | oeisdata/seq/A002/A002129.seq | ffe2ec7899925a65ff1df0f430513f80 |
A002130 | Generalized sum of divisors function. | [
"1",
"-1",
"1",
"3",
"-2",
"1",
"-5",
"23",
"-25",
"27",
"-49",
"74",
"-62",
"85",
"-132",
"165",
"-195",
"229",
"-240",
"325",
"-374",
"379",
"-469",
"553",
"-590",
"746",
"-805",
"854",
"-1000",
"1085",
"-1168",
"1284",
"-1396",
"1668",
"-1767",
... | [
"sign",
"easy"
] | 25 | 3 | 4 | [
"A002130",
"A060044"
] | [
"M2238",
"N0888"
] | N. J. A. Sloane | 2021-12-24T02:31:14 | oeisdata/seq/A002/A002130.seq | da28dfaa5eb02be09f3fd3d91b6824a4 |
A002131 | Sum of divisors d of n such that n/d is odd. | [
"1",
"2",
"4",
"4",
"6",
"8",
"8",
"8",
"13",
"12",
"12",
"16",
"14",
"16",
"24",
"16",
"18",
"26",
"20",
"24",
"32",
"24",
"24",
"32",
"31",
"28",
"40",
"32",
"30",
"48",
"32",
"32",
"48",
"36",
"48",
"52",
"38",
"40",
"56",
"48",
"42"... | [
"nonn",
"nice",
"easy",
"mult"
] | 132 | 1 | 2 | [
"A000203",
"A000593",
"A002131",
"A006519",
"A008438",
"A026741",
"A060047",
"A143119",
"A192065",
"A244051",
"A301798",
"A326938"
] | [
"M0937",
"N0351"
] | N. J. A. Sloane, Simon Plouffe | 2025-05-29T11:09:57 | oeisdata/seq/A002/A002131.seq | 9d13eae515626448cbb0430e7a855dac |
A002132 | Generalized sum of divisors function. | [
"1",
"2",
"4",
"8",
"14",
"18",
"28",
"40",
"52",
"70",
"88",
"104",
"140",
"168",
"196",
"240",
"278",
"320",
"380",
"440",
"504",
"562",
"644",
"720",
"808",
"910",
"1000",
"1120",
"1240",
"1360",
"1488",
"1600",
"1789",
"1938",
"2100",
"2296",... | [
"nonn",
"easy"
] | 34 | 4 | 2 | [
"A002132",
"A015128",
"A060047"
] | [
"M1096",
"N0418"
] | N. J. A. Sloane | 2025-11-05T15:21:41 | oeisdata/seq/A002/A002132.seq | d20c23b3e8966c325df5075f5afa2370 |
A002133 | Number of partitions of n with exactly two part sizes. | [
"0",
"0",
"1",
"2",
"5",
"6",
"11",
"13",
"17",
"22",
"27",
"29",
"37",
"44",
"44",
"55",
"59",
"68",
"71",
"81",
"82",
"102",
"97",
"112",
"109",
"136",
"126",
"149",
"141",
"168",
"157",
"188",
"176",
"212",
"182",
"231",
"207",
"254",
"2... | [
"nonn",
"look",
"easy"
] | 70 | 1 | 4 | [
"A002133",
"A002134",
"A060177"
] | [
"M1324",
"N0507"
] | N. J. A. Sloane | 2025-08-30T09:48:36 | oeisdata/seq/A002/A002133.seq | e80791701ad4105372bc67a2f4aa11ff |
A002134 | Generalized divisor function. Number of partitions of n with exactly three part sizes. | [
"1",
"2",
"5",
"10",
"15",
"25",
"37",
"52",
"67",
"97",
"117",
"154",
"184",
"235",
"277",
"338",
"385",
"469",
"531",
"630",
"698",
"810",
"910",
"1038",
"1144",
"1295",
"1425",
"1577",
"1741",
"1938",
"2089",
"2301",
"2505",
"2700",
"2970",
"3... | [
"nonn",
"easy"
] | 41 | 6 | 2 | [
"A002134",
"A060177",
"A116608"
] | [
"M1367",
"N0530"
] | N. J. A. Sloane | 2023-09-15T18:45:54 | oeisdata/seq/A002/A002134.seq | 97e03fcdf11d1bd6b1f12164d6221083 |
A002135 | Number of terms in a symmetrical determinant: a(n) = n*a(n-1) - (n-1)*(n-2)*a(n-3)/2. | [
"1",
"1",
"2",
"5",
"17",
"73",
"388",
"2461",
"18155",
"152531",
"1436714",
"14986879",
"171453343",
"2134070335",
"28708008128",
"415017867707",
"6416208498137",
"105630583492969",
"1844908072865290",
"34071573484225549",
"663368639907213281",
"13580208904207073801"
] | [
"nonn",
"nice",
"easy"
] | 130 | 0 | 3 | [
"A001147",
"A001710",
"A002135",
"A002137",
"A007717",
"A037143",
"A059422",
"A059423",
"A059424",
"A215771",
"A257463",
"A260338",
"A319225",
"A319226",
"A320655",
"A320656",
"A333467"
] | [
"M1513",
"N0594"
] | N. J. A. Sloane | 2025-11-05T15:35:24 | oeisdata/seq/A002/A002135.seq | ec1ed069f999401a5ec4c081bdcac48c |
A002136 | Matrices with 2 rows. | [
"1",
"2",
"6",
"23",
"109",
"618",
"4096",
"31133",
"267219",
"2557502",
"27011734",
"312115953",
"3916844779",
"53053052462",
"771450742596",
"11986779006647",
"198204672604489",
"3475110017769282",
"64396888392712366",
"1257612452945760503",
"25815617698822423341",
"55570... | [
"nonn"
] | 36 | 3 | 2 | null | [
"M1668",
"N0656"
] | N. J. A. Sloane | 2025-05-01T01:34:57 | oeisdata/seq/A002/A002136.seq | 87873e4950ad6cc978a83b05a5eca0cf |
A002137 | Number of n X n symmetric matrices with nonnegative integer entries, trace 0 and all row sums 2. | [
"1",
"0",
"1",
"1",
"6",
"22",
"130",
"822",
"6202",
"52552",
"499194",
"5238370",
"60222844",
"752587764",
"10157945044",
"147267180508",
"2282355168060",
"37655004171808",
"658906772228668",
"12188911634495388",
"237669544014377896",
"4871976826254018760",
"104742902332... | [
"nonn",
"nice",
"easy"
] | 112 | 0 | 5 | [
"A000985",
"A000986",
"A002135",
"A002137",
"A260340",
"A333351"
] | [
"M4154",
"N1726"
] | N. J. A. Sloane | 2025-11-02T03:34:24 | oeisdata/seq/A002/A002137.seq | c06d75ec6cada58e8078dc09015090b7 |
A002138 | 6th powers written backwards. | [
"0",
"1",
"46",
"927",
"6904",
"52651",
"65664",
"946711",
"441262",
"144135",
"1",
"1651771",
"4895892",
"9086284",
"6359257",
"52609311",
"61277761",
"96573142",
"42221043",
"18854074",
"46",
"12166758",
"409973311",
"988530841",
"679201191",
"526041442",
"67751... | [
"nonn",
"base",
"look"
] | 13 | 0 | 3 | null | null | N. J. A. Sloane | 2023-10-14T23:43:14 | oeisdata/seq/A002/A002138.seq | e713bef761922935d37cd4b45ec054e1 |
A002139 | Shuffling 2n cards. | [
"2",
"3",
"5",
"12",
"14",
"11",
"13",
"20",
"72",
"19",
"42",
"132",
"84",
"114",
"29",
"30",
"110",
"156",
"37",
"156",
"420",
"210",
"156",
"552",
"462",
"72",
"53",
"420",
"342",
"59",
"61",
"42",
"156",
"67",
"506",
"1260",
"90",
"420",
... | [
"nonn",
"nice"
] | 23 | 1 | 1 | [
"A002139",
"A002326"
] | [
"M0737",
"N0276"
] | N. J. A. Sloane | 2017-06-18T08:49:54 | oeisdata/seq/A002/A002139.seq | 0339b5a2a5b7d14b956af57176a7a6b8 |
A002140 | 7th powers written backwards. | [
"0",
"1",
"821",
"7812",
"48361",
"52187",
"639972",
"345328",
"2517902",
"9692874",
"1",
"17178491",
"80813853",
"71584726",
"405314501",
"573958071",
"654534862",
"376833014",
"230022216",
"937178398",
"821",
"1458801081",
"8887534942",
"7445284043",
"4241746854",
... | [
"nonn",
"base",
"look"
] | 19 | 0 | 3 | null | null | N. J. A. Sloane | 2023-10-14T23:43:34 | oeisdata/seq/A002/A002140.seq | 6b86f836ce2314e23622524f1743ed7e |
A002141 | Class numbers of quadratic fields. | [
"1",
"1",
"5",
"6",
"7",
"7",
"9",
"53",
"60",
"66",
"83",
"83",
"136",
"136",
"185",
"185",
"185",
"312",
"312",
"312",
"3064",
"3718",
"3718",
"3718",
"8096",
"9826",
"12384",
"16602",
"16602",
"16602",
"16760",
"16760",
"182424",
"323392",
"3233... | [
"nonn"
] | 20 | 3 | 3 | null | [
"M3745",
"N1530"
] | N. J. A. Sloane | 2023-10-14T23:44:12 | oeisdata/seq/A002/A002141.seq | 9150049c8eb38aff5f7f8104ea895671 |
A002142 | Primes p == 1 (mod 4) where class number of Q(sqrt p) increases. | [
"5",
"229",
"401",
"577",
"1129",
"1297",
"7057",
"8761",
"14401",
"32401",
"41617",
"57601",
"90001"
] | [
"nonn"
] | 16 | 1 | 1 | null | [
"M4032",
"N1673"
] | N. J. A. Sloane | 2023-10-14T23:44:46 | oeisdata/seq/A002/A002142.seq | 075c568edeffdfb38e339162a7eec7f2 |
A002143 | Class numbers h(-p) where p runs through the primes p == 3 (mod 4). | [
"1",
"1",
"1",
"1",
"3",
"3",
"1",
"5",
"3",
"1",
"7",
"5",
"3",
"5",
"3",
"5",
"5",
"3",
"7",
"1",
"11",
"5",
"13",
"9",
"3",
"7",
"5",
"15",
"7",
"13",
"11",
"3",
"3",
"19",
"3",
"5",
"19",
"9",
"3",
"17",
"9",
"21",
"15",
"5",
... | [
"nonn"
] | 63 | 1 | 5 | [
"A002143",
"A002145",
"A002146",
"A101435"
] | [
"M2266",
"N0896"
] | N. J. A. Sloane | 2025-12-09T21:33:49 | oeisdata/seq/A002/A002143.seq | 757c7d675c607c7b9104a9f6fb929b65 |
A002144 | Pythagorean primes: primes of the form 4*k + 1. | [
"5",
"13",
"17",
"29",
"37",
"41",
"53",
"61",
"73",
"89",
"97",
"101",
"109",
"113",
"137",
"149",
"157",
"173",
"181",
"193",
"197",
"229",
"233",
"241",
"257",
"269",
"277",
"281",
"293",
"313",
"317",
"337",
"349",
"353",
"373",
"389",
"397... | [
"nonn",
"easy",
"nice"
] | 512 | 1 | 1 | [
"A002144",
"A002145",
"A002313",
"A002314",
"A002476",
"A002972",
"A002973",
"A003658",
"A004431",
"A004613",
"A005098",
"A007519",
"A010051",
"A016813",
"A020668",
"A076339",
"A094407",
"A114200",
"A133870",
"A142925",
"A152676",
"A152680",
"A173330",
"A173331",
"A20... | [
"M3823",
"N1566"
] | N. J. A. Sloane | 2025-11-26T14:45:27 | oeisdata/seq/A002/A002144.seq | 15d90ab6200e6dbf3681b898104097ae |
A002145 | Primes of the form 4*k + 3. | [
"3",
"7",
"11",
"19",
"23",
"31",
"43",
"47",
"59",
"67",
"71",
"79",
"83",
"103",
"107",
"127",
"131",
"139",
"151",
"163",
"167",
"179",
"191",
"199",
"211",
"223",
"227",
"239",
"251",
"263",
"271",
"283",
"307",
"311",
"331",
"347",
"359",
... | [
"nonn",
"easy"
] | 325 | 1 | 1 | [
"A000032",
"A000408",
"A002144",
"A002145",
"A003657",
"A004614",
"A005098",
"A016105",
"A016754",
"A045326",
"A085992",
"A095278",
"A122869",
"A122870",
"A334912"
] | [
"M2624",
"N1039"
] | N. J. A. Sloane | 2025-09-26T09:17:05 | oeisdata/seq/A002/A002145.seq | 745f57816d004d2b44310dd66f0b8657 |
A002146 | Smallest prime == 7 (mod 8) where Q(sqrt(-p)) has class number 2n+1. | [
"7",
"23",
"47",
"71",
"199",
"167",
"191",
"239",
"383",
"311",
"431",
"647",
"479",
"983",
"887",
"719",
"839",
"1031",
"1487",
"1439",
"1151",
"1847",
"1319",
"3023",
"1511",
"1559",
"2711",
"4463",
"2591",
"2399",
"3863",
"2351",
"3527",
"3719"
] | [
"nonn"
] | 32 | 0 | 1 | [
"A002143",
"A002146",
"A002147",
"A002148",
"A060651"
] | [
"M4377",
"N1841"
] | N. J. A. Sloane, Mira Bernstein | 2022-08-06T07:17:22 | oeisdata/seq/A002/A002146.seq | e96e223d9f9c27128756494b89e28ba3 |
A002147 | Largest prime == 7 (mod 8) with class number 2n+1. | [
"7",
"31",
"127",
"487",
"1423",
"1303",
"2143",
"2647",
"4447",
"5527",
"5647",
"6703",
"5503",
"11383",
"8863",
"13687",
"13183",
"12007",
"22807",
"18127",
"21487",
"22303",
"29863",
"25303",
"27127"
] | [
"nonn"
] | 21 | 0 | 1 | [
"A002146",
"A002147"
] | [
"M4402",
"N1857"
] | N. J. A. Sloane | 2022-08-06T07:17:52 | oeisdata/seq/A002/A002147.seq | c139785d6a05132e33f004affe1cbe1d |
A002148 | Smallest prime p==3 (mod 8) such that Q(sqrt(-p)) has class number 2n+1. | [
"3",
"59",
"131",
"251",
"419",
"659",
"1019",
"971",
"1091",
"2099",
"1931",
"1811",
"3851",
"3299",
"2939",
"3251",
"4091",
"4259",
"8147",
"5099",
"9467",
"6299",
"6971",
"8291",
"8819",
"14771",
"22619",
"9539",
"13331",
"18443",
"11171",
"16979",
... | [
"nonn"
] | 29 | 0 | 1 | [
"A002143",
"A002148",
"A002149",
"A003173",
"A006203"
] | [
"M3164",
"N1282"
] | N. J. A. Sloane and Mira Bernstein | 2022-08-06T07:17:33 | oeisdata/seq/A002/A002148.seq | de81b5002ac15f26b02baac498f44b95 |
A002149 | Largest prime p==3 (mod 8) such that Q(sqrt(-p)) has class number 2n+1. | [
"163",
"907",
"2683",
"5923",
"10627",
"15667",
"20563",
"34483",
"37123",
"38707",
"61483",
"90787",
"93307",
"103387",
"166147",
"133387",
"222643",
"210907",
"158923",
"253507",
"296587"
] | [
"nonn"
] | 26 | 0 | 1 | [
"A002148",
"A002149",
"A003173",
"A006203"
] | [
"M5407",
"N2350"
] | N. J. A. Sloane | 2022-08-06T07:17:56 | oeisdata/seq/A002/A002149.seq | fbd2a72b57ec554956cefe79feccd28d |
A002150 | Numbers k for which the rank of the elliptic curve y^2 = x^3 - k is 0. | [
"1",
"3",
"5",
"6",
"8",
"9",
"10",
"12",
"14",
"16",
"17",
"24",
"27",
"31",
"32",
"33",
"34",
"36",
"37",
"41",
"42",
"46",
"52",
"62",
"64",
"68",
"69",
"70",
"73",
"77",
"78",
"80",
"82",
"86",
"88",
"90",
"92",
"96",
"97",
"98",
"9... | [
"nonn"
] | 35 | 1 | 2 | [
"A002150",
"A002152",
"A002154",
"A060951",
"A179136",
"A179137"
] | [
"M2391",
"N0949"
] | N. J. A. Sloane | 2023-10-14T17:21:55 | oeisdata/seq/A002/A002150.seq | 48550487be467a811a7edd171d3c28e9 |
A002151 | Numbers k for which rank of the elliptic curve y^2 = x^3 + k is 0. | [
"1",
"4",
"6",
"7",
"13",
"14",
"16",
"20",
"21",
"23",
"25",
"27",
"29",
"32",
"34",
"42",
"45",
"49",
"51",
"53",
"59",
"60",
"64",
"70",
"75",
"78",
"81",
"84",
"85",
"86",
"87",
"88",
"90",
"93",
"95",
"96",
"104",
"109",
"114",
"115"... | [
"nonn"
] | 38 | 1 | 2 | [
"A002151",
"A002153",
"A002155",
"A060748",
"A060838",
"A060950",
"A060951",
"A060952",
"A060953",
"A102833"
] | [
"M3271",
"N1321"
] | N. J. A. Sloane | 2023-10-14T17:22:28 | oeisdata/seq/A002/A002151.seq | 039a33cb96ad5836c6008e02a4649dbb |
A002152 | Numbers k for which the rank of the elliptic curve y^2 = x^3 - k is 1. | [
"2",
"4",
"7",
"13",
"15",
"18",
"19",
"20",
"21",
"22",
"23",
"25",
"28",
"29",
"30",
"35",
"38",
"40",
"43",
"44",
"45",
"48",
"49",
"50",
"51",
"54",
"55",
"56",
"57",
"58",
"59",
"60",
"63",
"65",
"66",
"71",
"72",
"74",
"75",
"79",
... | [
"nonn"
] | 32 | 1 | 1 | null | [
"M1065",
"N0401"
] | N. J. A. Sloane | 2023-10-14T23:51:22 | oeisdata/seq/A002/A002152.seq | a046772a7bd5a772bd45545e4e2300f0 |
A002153 | Numbers k for which the rank of the elliptic curve y^2 = x^3 + k is 1. | [
"2",
"3",
"5",
"8",
"9",
"10",
"11",
"12",
"18",
"19",
"22",
"26",
"28",
"30",
"31",
"33",
"35",
"36",
"38",
"39",
"40",
"41",
"44",
"46",
"47",
"48",
"50",
"52",
"54",
"55",
"56",
"58",
"61",
"62",
"66",
"67",
"68",
"69",
"71",
"72",
"... | [
"nonn"
] | 34 | 1 | 1 | [
"A002151",
"A002153",
"A002155",
"A060748",
"A060838",
"A060950",
"A060951",
"A060953",
"A102833"
] | [
"M0682",
"N0251"
] | N. J. A. Sloane | 2024-07-06T12:02:28 | oeisdata/seq/A002/A002153.seq | 286be040101206c0f21fa1f1761e2242 |
A002154 | Numbers k for which the rank of the elliptic curve y^2 = x^3 - k is 2. | [
"11",
"26",
"39",
"47",
"53",
"61",
"67",
"76",
"83",
"89",
"104",
"106",
"109",
"116",
"118",
"121",
"139",
"147",
"152",
"155",
"170",
"186",
"191",
"200",
"207",
"211",
"212",
"214",
"219",
"222",
"233",
"236",
"244",
"249",
"262",
"277",
"2... | [
"nonn"
] | 32 | 1 | 1 | null | [
"M4782",
"N2040"
] | N. J. A. Sloane | 2023-10-14T23:49:16 | oeisdata/seq/A002/A002154.seq | a75593ae510a69488480be49ec90a18f |
A002155 | Numbers k for which the rank of the elliptic curve y^2 = x^3 + k is 2. | [
"15",
"17",
"24",
"37",
"43",
"57",
"63",
"65",
"73",
"79",
"89",
"101",
"106",
"122",
"129",
"131",
"142",
"145",
"148",
"151",
"161",
"164",
"168",
"171",
"186",
"195",
"197",
"198",
"204",
"217",
"222",
"223",
"225",
"229",
"232",
"233",
"24... | [
"nonn"
] | 35 | 1 | 1 | [
"A002151",
"A002153",
"A002155",
"A060748",
"A060838",
"A060950",
"A060951",
"A060953",
"A102833"
] | [
"M4957",
"N2125"
] | N. J. A. Sloane | 2024-07-06T12:02:28 | oeisdata/seq/A002/A002155.seq | 7bdfad83167ddfd8fecee177b07d751b |
A002156 | Numbers k for which the rank of the elliptic curve y^2 = x^3 - k*x is 0. | [
"1",
"3",
"4",
"8",
"9",
"11",
"13",
"16",
"18",
"19",
"24",
"27",
"28",
"29",
"33",
"35",
"40",
"43",
"44",
"48",
"51",
"59",
"61",
"63",
"64",
"67",
"68",
"75",
"81",
"83",
"88",
"91",
"92",
"93",
"98",
"100",
"104",
"107",
"108",
"109"... | [
"nonn"
] | 34 | 1 | 2 | [
"A002156",
"A060952"
] | [
"M2345",
"N0926"
] | N. J. A. Sloane | 2023-10-14T15:58:38 | oeisdata/seq/A002/A002156.seq | fffaad6bd330d2849ba20ac35fc8d6a2 |
A002157 | Numbers k for which the rank of the elliptic curve y^2 = x^3 - k*x is 1. | [
"2",
"5",
"6",
"7",
"10",
"12",
"14",
"15",
"20",
"21",
"22",
"23",
"25",
"26",
"30",
"31",
"32",
"34",
"36",
"37",
"38",
"39",
"41",
"42",
"45",
"46",
"47",
"49",
"50",
"52",
"53",
"54",
"55",
"57",
"58",
"60",
"62",
"66",
"69",
"70",
... | [
"nonn"
] | 28 | 1 | 1 | [
"A002157",
"A060952"
] | [
"M1317",
"N0505"
] | N. J. A. Sloane | 2023-10-15T13:15:37 | oeisdata/seq/A002/A002157.seq | 6c26d6f98e6217e2272460834d9e92c4 |
A002158 | Numbers k for which the rank of the elliptic curve y^2 = x^3 + k*x is 0. | [
"1",
"2",
"4",
"6",
"7",
"10",
"11",
"12",
"16",
"17",
"22",
"23",
"25",
"26",
"27",
"30",
"32",
"36",
"38",
"41",
"42",
"43",
"44",
"45",
"50",
"52",
"54",
"57",
"58",
"59",
"62",
"64",
"70",
"71",
"72",
"74",
"75",
"76",
"78",
"81",
"... | [
"nonn"
] | 29 | 1 | 2 | [
"A002158",
"A002159",
"A060953",
"A076329"
] | [
"M0981",
"N0369"
] | N. J. A. Sloane | 2023-10-14T16:00:10 | oeisdata/seq/A002/A002158.seq | 332d4b926a21369e3a5b1e08c2033b70 |
A002159 | Numbers k for which the rank of the elliptic curve y^2 = x^3 + k*x is 1. | [
"3",
"5",
"8",
"9",
"13",
"15",
"18",
"19",
"20",
"21",
"24",
"28",
"29",
"31",
"35",
"37",
"40",
"47",
"48",
"49",
"51",
"53",
"56",
"60",
"61",
"67",
"69",
"77",
"79",
"80",
"83",
"84",
"85",
"88",
"90",
"92",
"93",
"95",
"98",
"100",
... | [
"nonn"
] | 32 | 1 | 1 | [
"A002159",
"A060953",
"A076329"
] | [
"M2429",
"N0962"
] | N. J. A. Sloane | 2023-10-14T16:01:22 | oeisdata/seq/A002/A002159.seq | 7e2c23e51921319ad5c73d3af659cb48 |
A002160 | Nearest integer to Pi^n. | [
"1",
"3",
"10",
"31",
"97",
"306",
"961",
"3020",
"9489",
"29809",
"93648",
"294204",
"924269",
"2903677",
"9122171",
"28658146",
"90032221",
"282844564",
"888582403",
"2791563950",
"8769956796",
"27551631843",
"86556004192",
"271923706894",
"854273519914",
"2683779... | [
"nonn",
"easy"
] | 29 | 0 | 2 | [
"A000227",
"A001672",
"A001673",
"A002160"
] | [
"M2841",
"N1142"
] | N. J. A. Sloane | 2025-09-22T16:00:16 | oeisdata/seq/A002/A002160.seq | 6f5416f039c12568b4c2ba5f80f8e401 |
A002161 | Decimal expansion of square root of Pi. | [
"1",
"7",
"7",
"2",
"4",
"5",
"3",
"8",
"5",
"0",
"9",
"0",
"5",
"5",
"1",
"6",
"0",
"2",
"7",
"2",
"9",
"8",
"1",
"6",
"7",
"4",
"8",
"3",
"3",
"4",
"1",
"1",
"4",
"5",
"1",
"8",
"2",
"7",
"9",
"7",
"5",
"4",
"9",
"4",
"5",
"... | [
"nonn",
"cons"
] | 98 | 1 | 2 | [
"A000796",
"A002161",
"A002388",
"A068466",
"A073005",
"A073006",
"A175379",
"A175380",
"A195907",
"A203142",
"A203145",
"A220086"
] | [
"M4332",
"N1814"
] | N. J. A. Sloane | 2025-06-06T08:36:46 | oeisdata/seq/A002/A002161.seq | 69934755a0450f943e601cca10550b1a |
A002162 | Decimal expansion of the natural logarithm of 2. | [
"6",
"9",
"3",
"1",
"4",
"7",
"1",
"8",
"0",
"5",
"5",
"9",
"9",
"4",
"5",
"3",
"0",
"9",
"4",
"1",
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"2",
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"2",
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"2",
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"8",
"1",
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"6",
"5",
"6",
"8",
"0",
"7",
"5",
"5",
"0",
"0",
"1",
"3",
"4",
"... | [
"nonn",
"cons",
"changed"
] | 340 | 0 | 1 | [
"A002162",
"A002939",
"A008288",
"A016730",
"A142979",
"A142992"
] | [
"M4074",
"N1689"
] | N. J. A. Sloane | 2026-01-18T14:12:50 | oeisdata/seq/A002/A002162.seq | d2837b27bd7cb49dcc3e3a168e1ffc62 |
A002163 | Decimal expansion of square root of 5. | [
"2",
"2",
"3",
"6",
"0",
"6",
"7",
"9",
"7",
"7",
"4",
"9",
"9",
"7",
"8",
"9",
"6",
"9",
"6",
"4",
"0",
"9",
"1",
"7",
"3",
"6",
"6",
"8",
"7",
"3",
"1",
"2",
"7",
"6",
"2",
"3",
"5",
"4",
"4",
"0",
"6",
"1",
"8",
"3",
"5",
"... | [
"nonn",
"cons"
] | 150 | 1 | 1 | [
"A000032",
"A000045",
"A001622",
"A002163",
"A040002",
"A104457"
] | [
"M0293",
"N0105"
] | N. J. A. Sloane | 2025-12-22T15:46:25 | oeisdata/seq/A002/A002163.seq | c6806b1b2b3c30397b48805c602453f6 |
A002164 | E.g.f.: high-temperature series in J/2kT for logarithm of partition function for the spin-1/2 linear (1D) Heisenberg model. | [
"0",
"3",
"-6",
"-30",
"360",
"504",
"-44016",
"204048",
"8261760",
"-128422272",
"-1816480512",
"76562054400",
"124207469568",
"-51042832542720",
"580686719698944",
"36632422458820608",
"-1141184282933624832",
"-23612862502431719424",
"1881307594631033978880",
"253019693533000... | [
"sign"
] | 25 | 1 | 2 | [
"A002164",
"A005399"
] | [
"M2601",
"N1028"
] | N. J. A. Sloane | 2022-02-24T08:19:17 | oeisdata/seq/A002/A002164.seq | 3c335ebe6fba8d1343fa6a1135b3df40 |
A002165 | High temperature series for spin-1/2 Heisenberg specific heat on 3-dimensional f.c.c. lattice. | [
"0",
"18",
"108",
"180",
"-5040",
"162000",
"14565600",
"563253408",
"17544639744",
"750412309248",
"56646776913408",
"4973976625190400",
"421817449494804480"
] | [
"sign",
"more"
] | 34 | 1 | 2 | [
"A002165",
"A002166",
"A002167",
"A002169"
] | [
"M5057",
"N2187"
] | N. J. A. Sloane | 2023-10-09T11:30:03 | oeisdata/seq/A002/A002165.seq | 62ead277ccee71b172747f4bbdf70739 |
A002166 | Susceptibility series for f.c.c. lattice. | [
"12",
"240",
"6624",
"234720",
"10208832",
"526810176",
"31434585600",
"2127785025024",
"161064469168128",
"13483480670745600",
"1237073710591635456",
"123437675536945410048",
"13308034251238570770432",
"1541580126710320881573888"
] | [
"nonn",
"more"
] | 19 | 1 | 1 | null | [
"M4877",
"N2090"
] | N. J. A. Sloane | 2021-10-21T01:07:13 | oeisdata/seq/A002/A002166.seq | d7a5798cf22933082498417c3e262724 |
A002167 | High temperature series for spin-1/2 Heisenberg specific heat on 3-dimensional b.c.c. lattice. | [
"0",
"12",
"-24",
"168",
"1440",
"24480",
"-297024",
"28017216",
"-533681664",
"41156316672",
"-503287538688",
"53001415916544",
"-1839416689004544",
"246102905022713856",
"-9001661201883684864"
] | [
"sign",
"more"
] | 34 | 1 | 2 | [
"A002165",
"A002167",
"A002168",
"A002169"
] | [
"M4830",
"N2066"
] | N. J. A. Sloane | 2023-10-09T11:30:21 | oeisdata/seq/A002/A002167.seq | b9d316c2f45256b90da83c476a8ea988 |
A002168 | High-temperature series for spin-1/2 Heisenberg susceptibility on b.c.c. lattice. | [
"1",
"8",
"96",
"1664",
"36800",
"1008768",
"32626560",
"1221399040",
"51734584320",
"2459086364672",
"129082499311616",
"7432690738003968",
"464885622793134080",
"31456185663820136448",
"2284815238218471260160",
"177611252880786297913344"
] | [
"nonn",
"more"
] | 35 | 0 | 2 | [
"A002167",
"A002168"
] | [
"M4566",
"N1943"
] | N. J. A. Sloane | 2023-10-09T11:30:35 | oeisdata/seq/A002/A002168.seq | f1dbe3dc34cdee2c676896535d8a4a7c |
A002169 | High temperature series for spin-1/2 Heisenberg specific heat on 3-dimensional simple cubic lattice. | [
"0",
"9",
"-18",
"-162",
"2520",
"33192",
"-1019088",
"-7804944",
"723961728",
"2596523904",
"-856142090496",
"6383648984832",
"1356696930401280",
"-27667884260938752",
"-2908030732698175488",
"122264703581556307968",
"7238339805811283361792"
] | [
"sign",
"more"
] | 43 | 1 | 2 | [
"A002165",
"A002167",
"A002169",
"A002170",
"A002916",
"A002922",
"A005402"
] | [
"M4602",
"N1963"
] | N. J. A. Sloane | 2023-10-09T11:29:47 | oeisdata/seq/A002/A002169.seq | f851b7bc27c5f6455648994bb3458761 |
A002170 | High temperature series for spin-1/2 Heisenberg susceptibility on 3-dimensional simple cubic lattice. | [
"6",
"48",
"528",
"7920",
"149856",
"3169248",
"77046528",
"2231209728",
"71938507776",
"2446325534208",
"92886269386752",
"3995799894239232",
"180512165153832960",
"8443006907441565696",
"440473891771339603968",
"25125124946211876962304",
"1444211070518302580146176"
] | [
"nonn",
"more"
] | 31 | 1 | 1 | [
"A002169",
"A002170"
] | [
"M4257",
"N1778"
] | N. J. A. Sloane | 2023-10-09T11:30:53 | oeisdata/seq/A002/A002170.seq | 9f7206dbddf0fd20ccb65c92cf14aec2 |
A002171 | Glaisher's chi numbers. a(n) = chi(4*n + 1). | [
"1",
"-2",
"-3",
"6",
"2",
"0",
"-1",
"-10",
"0",
"-2",
"10",
"6",
"-7",
"14",
"0",
"-10",
"-12",
"0",
"-6",
"0",
"9",
"-4",
"10",
"0",
"18",
"-2",
"0",
"6",
"-14",
"-18",
"-11",
"12",
"0",
"0",
"-22",
"0",
"20",
"14",
"-6",
"22",
"0",
... | [
"sign",
"easy",
"nice"
] | 98 | 0 | 2 | [
"A000203",
"A002171",
"A002172",
"A278720",
"A279955"
] | [
"M0745",
"N0280"
] | N. J. A. Sloane | 2025-09-15T00:14:30 | oeisdata/seq/A002/A002171.seq | cf73b55fee1d7076c9b67c34750eb5c8 |
A002172 | Glaisher's chi numbers chi(p) for p a prime of the form 4m+1. | [
"-2",
"6",
"2",
"-10",
"-2",
"10",
"14",
"-10",
"-6",
"10",
"18",
"-2",
"6",
"-14",
"-22",
"14",
"22",
"-26",
"-18",
"-14",
"-2",
"30",
"26",
"-30",
"2",
"-26",
"-18",
"10",
"-34",
"26",
"22",
"18",
"-10",
"34",
"14",
"-34",
"38",
"2",
"-6"... | [
"nice",
"sign"
] | 34 | 1 | 1 | [
"A002171",
"A002172"
] | [
"M1556",
"N0607"
] | N. J. A. Sloane | 2017-10-02T03:08:09 | oeisdata/seq/A002/A002172.seq | 43e4271b7f181a8a34b0c2196530ad11 |
A002173 | a(n) = Sum_{d|n, d == 1 mod 4} d^2 - Sum_{d|n, d == 3 mod 4} d^2. | [
"1",
"1",
"-8",
"1",
"26",
"-8",
"-48",
"1",
"73",
"26",
"-120",
"-8",
"170",
"-48",
"-208",
"1",
"290",
"73",
"-360",
"26",
"384",
"-120",
"-528",
"-8",
"651",
"170",
"-656",
"-48",
"842",
"-208",
"-960",
"1",
"960",
"290",
"-1248",
"73",
"137... | [
"sign",
"easy",
"mult",
"look"
] | 81 | 1 | 3 | [
"A002173",
"A050450",
"A050453",
"A056594",
"A120030"
] | [
"M4467",
"N1895"
] | N. J. A. Sloane | 2025-12-13T03:49:24 | oeisdata/seq/A002/A002173.seq | 513694e20a8b7c331a6db46e7dedd99a |
A002174 | Values taken by reduced totient function psi(n). | [
"1",
"2",
"4",
"6",
"8",
"10",
"12",
"16",
"18",
"20",
"22",
"24",
"28",
"30",
"32",
"36",
"40",
"42",
"44",
"46",
"48",
"52",
"54",
"56",
"58",
"60",
"64",
"66",
"70",
"72",
"78",
"80",
"82",
"84",
"88",
"90",
"92",
"96",
"100",
"102",
... | [
"nonn",
"nice"
] | 52 | 1 | 2 | [
"A002174",
"A002322",
"A002396",
"A143407",
"A143408"
] | [
"M0986",
"N0370"
] | N. J. A. Sloane | 2017-07-03T11:43:02 | oeisdata/seq/A002/A002174.seq | 75672940bf9c04e51319bcc790708af8 |
A002175 | Excess of number of divisors of 12n+1 of form 4k+1 over those of form 4k+3. | [
"1",
"2",
"3",
"2",
"1",
"2",
"2",
"4",
"2",
"2",
"1",
"0",
"4",
"2",
"3",
"2",
"2",
"4",
"0",
"2",
"2",
"0",
"4",
"2",
"3",
"0",
"2",
"6",
"2",
"2",
"1",
"2",
"0",
"2",
"2",
"2",
"2",
"4",
"2",
"0",
"4",
"4",
"4",
"0",
"1",
"... | [
"nonn"
] | 50 | 0 | 2 | [
"A002175",
"A002654",
"A008441",
"A008442",
"A035154",
"A035181",
"A035184",
"A112301",
"A113406",
"A113652",
"A116604",
"A121363",
"A121450",
"A122856",
"A122864",
"A122865",
"A125061",
"A125079",
"A129447",
"A129448",
"A132004",
"A134013",
"A134015",
"A138741",
"A13... | [
"M0416",
"N0159"
] | N. J. A. Sloane | 2025-02-16T08:32:25 | oeisdata/seq/A002/A002175.seq | 02eda36883e5a254592b28a6d1727747 |
A002176 | a(n) = LCM of denominators of Cotesian numbers {C(n,k), 0 <= k <= n}. | [
"2",
"6",
"8",
"90",
"288",
"840",
"17280",
"28350",
"89600",
"598752",
"87091200",
"63063000",
"402361344000",
"5003856000",
"2066448384",
"976924698750",
"3766102179840000",
"15209113920000",
"5377993912811520000",
"1646485441080480",
"89903156428800000"
] | [
"nonn",
"nice",
"easy"
] | 29 | 1 | 1 | [
"A002176",
"A002177",
"A002179",
"A100620",
"A100621",
"A100640",
"A100641",
"A100642"
] | [
"M1569",
"N0612"
] | N. J. A. Sloane | 2022-01-29T01:14:16 | oeisdata/seq/A002/A002176.seq | b2f8d3a32c9db6b9220d9e256974ff14 |
A002177 | Numerators of Cotesian numbers (not in lowest terms): A002176(n)*C(n,0). | [
"1",
"1",
"1",
"7",
"19",
"41",
"751",
"989",
"2857",
"16067",
"2171465",
"1364651",
"8181904909",
"90241897",
"35310023",
"15043611773",
"55294720874657",
"203732352169",
"69028763155644023",
"19470140241329",
"1022779523247467",
"396760150748100749"
] | [
"nonn",
"easy",
"nice"
] | 26 | 1 | 4 | [
"A002176",
"A002177",
"A002179",
"A100620",
"A100621",
"A100640",
"A100641"
] | [
"M4364",
"N1829"
] | N. J. A. Sloane | 2022-01-29T01:14:29 | oeisdata/seq/A002/A002177.seq | daf8bbca500e90b12f5c61e78468f0bc |
A002178 | Numerators of Cotesian numbers (not in lowest terms): A002176*C(n,1). | [
"1",
"4",
"3",
"32",
"75",
"216",
"3577",
"5888",
"15741",
"106300",
"13486539",
"9903168",
"56280729661",
"710986864",
"265553865",
"127626606592",
"450185515446285",
"1848730221900",
"603652082270808125",
"187926090380000",
"9545933933230947"
] | [
"nonn",
"easy",
"nice"
] | 22 | 1 | 2 | [
"A002176",
"A002178",
"A002179",
"A100620",
"A100621",
"A100640",
"A100641"
] | [
"M3216",
"N1302"
] | N. J. A. Sloane | 2022-01-29T01:14:03 | oeisdata/seq/A002/A002178.seq | 4004b7a264911236fc0040e0e222f0a6 |
A002179 | Numerators of Cotesian numbers (not in lowest terms): A002176*C(n,2). | [
"0",
"1",
"3",
"12",
"50",
"27",
"1323",
"-928",
"1080",
"-48525",
"-3237113",
"-7587864",
"-31268252574",
"-770720657",
"-232936065",
"-179731134720",
"-542023437008852",
"-3212744374395",
"-926840515700222955",
"-389358194177500",
"-17858352159793110"
] | [
"sign",
"easy"
] | 23 | 2 | 3 | [
"A002176",
"A002177",
"A002178",
"A002179",
"A100620",
"A100621",
"A100640",
"A100641"
] | [
"M2921",
"N1172"
] | N. J. A. Sloane | 2023-10-14T21:15:32 | oeisdata/seq/A002/A002179.seq | 366fe2992a2110645344414930cecfe1 |
A002180 | Values taken by the half-totient function phi(m)/2. | [
"1",
"2",
"3",
"4",
"5",
"6",
"8",
"9",
"10",
"11",
"12",
"14",
"15",
"16",
"18",
"20",
"21",
"22",
"23",
"24",
"26",
"27",
"28",
"29",
"30",
"32",
"33",
"35",
"36",
"39",
"40",
"41",
"42",
"44",
"46",
"48",
"50",
"51",
"52",
"53",
"54"... | [
"nonn",
"nice",
"easy"
] | 42 | 2 | 2 | [
"A002180",
"A002202",
"A079695"
] | [
"M0500",
"N0180"
] | N. J. A. Sloane | 2018-05-08T15:11:53 | oeisdata/seq/A002/A002180.seq | e01f4262701eb91c8e9bfe68c39b259b |
A002181 | Least number k such that phi(k) = m, where m runs through the values (A002202) taken by phi. | [
"1",
"3",
"5",
"7",
"15",
"11",
"13",
"17",
"19",
"25",
"23",
"35",
"29",
"31",
"51",
"37",
"41",
"43",
"69",
"47",
"65",
"53",
"81",
"87",
"59",
"61",
"85",
"67",
"71",
"73",
"79",
"123",
"83",
"129",
"89",
"141",
"97",
"101",
"103",
"15... | [
"nonn"
] | 49 | 1 | 2 | [
"A002181",
"A002202",
"A006511",
"A058277",
"A061026",
"A387221"
] | [
"M2421",
"N0957"
] | N. J. A. Sloane | 2025-12-17T23:22:45 | oeisdata/seq/A002/A002181.seq | 31ce84e50a2264c1acafd3231abe4363 |
A002182 | Highly composite numbers: numbers n where d(n), the number of divisors of n (A000005), increases to a record. | [
"1",
"2",
"4",
"6",
"12",
"24",
"36",
"48",
"60",
"120",
"180",
"240",
"360",
"720",
"840",
"1260",
"1680",
"2520",
"5040",
"7560",
"10080",
"15120",
"20160",
"25200",
"27720",
"45360",
"50400",
"55440",
"83160",
"110880",
"166320",
"221760",
"277200",... | [
"nonn",
"nice"
] | 302 | 1 | 2 | [
"A000005",
"A002110",
"A002182",
"A002183",
"A002201",
"A002473",
"A002808",
"A003418",
"A004394",
"A006218",
"A025487",
"A037992",
"A068507",
"A072938",
"A094348",
"A106037",
"A108602",
"A108951",
"A112778",
"A112779",
"A112780",
"A112781",
"A126098",
"A161184",
"A19... | [
"M1025",
"N0385"
] | N. J. A. Sloane | 2025-11-05T15:35:24 | oeisdata/seq/A002/A002182.seq | 7fbdca534f90aefedbefba9e762d903f |
A002183 | Number of divisors of n-th highly composite number. | [
"1",
"2",
"3",
"4",
"6",
"8",
"9",
"10",
"12",
"16",
"18",
"20",
"24",
"30",
"32",
"36",
"40",
"48",
"60",
"64",
"72",
"80",
"84",
"90",
"96",
"100",
"108",
"120",
"128",
"144",
"160",
"168",
"180",
"192",
"200",
"216",
"224",
"240",
"256",... | [
"nonn",
"nice"
] | 72 | 1 | 2 | [
"A000005",
"A002182",
"A002183",
"A002201",
"A006218",
"A061799",
"A070319",
"A243220",
"A261100",
"A329605",
"A329902"
] | [
"M0546",
"N0196"
] | N. J. A. Sloane | 2025-08-12T11:43:07 | oeisdata/seq/A002/A002183.seq | 25db2ddb613858395a92b4971b2b4c01 |
A002184 | a(n) = least primitive factor of 2^(2n+1) - 1. | [
"1",
"7",
"31",
"127",
"73",
"23",
"8191",
"151",
"131071",
"524287",
"337",
"47",
"601",
"262657",
"233",
"2147483647",
"599479",
"71",
"223",
"79",
"13367",
"431",
"631",
"2351",
"4432676798593",
"103",
"6361",
"881",
"32377",
"179951",
"2305843009213693... | [
"nonn"
] | 33 | 0 | 2 | [
"A002184",
"A002588",
"A112927"
] | [
"M4400",
"N1855"
] | N. J. A. Sloane | 2022-04-26T21:48:40 | oeisdata/seq/A002/A002184.seq | 58ca3dfd4dbe4ded482549d6910b86aa |
A002185 | Smallest primitive factor of 2^(2n+1) + 1. | [
"3",
"1",
"11",
"43",
"19",
"683",
"2731",
"331",
"43691",
"174763",
"5419",
"2796203",
"251",
"87211",
"59",
"715827883",
"67",
"281",
"1777",
"22366891",
"83",
"2932031007403",
"18837001",
"283",
"4363953127297",
"307",
"107",
"2971",
"571",
"2833",
"768... | [
"nonn"
] | 27 | 0 | 1 | [
"A002185",
"A002589",
"A086257",
"A112927"
] | [
"M2233",
"N0885"
] | N. J. A. Sloane | 2025-02-25T23:16:39 | oeisdata/seq/A002/A002185.seq | de215bd8aa246a1294edb2155e64ca2e |
A002186 | Sprague-Grundy values for the game of Kayles (octal games .77 and .771). | [
"0",
"1",
"2",
"3",
"1",
"4",
"3",
"2",
"1",
"4",
"2",
"6",
"4",
"1",
"2",
"7",
"1",
"4",
"3",
"2",
"1",
"4",
"6",
"7",
"4",
"1",
"2",
"8",
"5",
"4",
"7",
"2",
"1",
"8",
"6",
"7",
"4",
"1",
"2",
"3",
"1",
"4",
"7",
"2",
"1",
"... | [
"nonn",
"nice",
"easy"
] | 41 | 0 | 3 | [
"A002186",
"A071074",
"A071434"
] | [
"M0410",
"N0156"
] | N. J. A. Sloane | 2022-01-29T01:13:29 | oeisdata/seq/A002/A002186.seq | 72fdf2938830a8b69d84b8c15a27ccac |
A002187 | Sprague-Grundy values for Dawson's Chess (octal game .137). | [
"0",
"1",
"1",
"2",
"0",
"3",
"1",
"1",
"0",
"3",
"3",
"2",
"2",
"4",
"0",
"5",
"2",
"2",
"3",
"3",
"0",
"1",
"1",
"3",
"0",
"2",
"1",
"1",
"0",
"4",
"5",
"2",
"7",
"4",
"0",
"1",
"1",
"2",
"0",
"3",
"1",
"1",
"0",
"3",
"3",
"... | [
"nonn",
"nice",
"easy",
"changed"
] | 30 | 0 | 4 | null | [
"M0025",
"N0007"
] | N. J. A. Sloane | 2026-01-05T13:34:13 | oeisdata/seq/A002/A002187.seq | 944d3c21b92b99d7252c73fcd6d783ce |
A002188 | Sprague-Grundy value for Grundy's game when starting with n tokens. | [
"0",
"0",
"0",
"1",
"0",
"2",
"1",
"0",
"2",
"1",
"0",
"2",
"1",
"3",
"2",
"1",
"3",
"2",
"4",
"3",
"0",
"4",
"3",
"0",
"4",
"3",
"0",
"4",
"1",
"2",
"3",
"1",
"2",
"4",
"1",
"2",
"4",
"1",
"2",
"4",
"1",
"5",
"4",
"1",
"5",
"... | [
"nonn",
"easy",
"look",
"nice"
] | 87 | 0 | 6 | [
"A002188",
"A036685",
"A180120",
"A180121"
] | [
"M0044",
"N0014"
] | N. J. A. Sloane | 2025-08-19T09:42:40 | oeisdata/seq/A002/A002188.seq | 4e3f8559c3f947ffdf8f29c2a4a40f3c |
A002189 | Pseudo-squares: a(n) = the least nonsquare positive integer which is 1 mod 8 and is a (nonzero) quadratic residue modulo the first n odd primes. | [
"17",
"73",
"241",
"1009",
"2641",
"8089",
"18001",
"53881",
"87481",
"117049",
"515761",
"1083289",
"3206641",
"3818929",
"9257329",
"22000801",
"48473881",
"48473881",
"175244281",
"427733329",
"427733329",
"898716289",
"2805544681",
"2805544681",
"2805544681"
] | [
"nonn",
"nice"
] | 71 | 0 | 1 | [
"A002189",
"A018883",
"A045535",
"A090983"
] | [
"M5039",
"N2175",
"N2326"
] | N. J. A. Sloane | 2025-11-05T15:21:41 | oeisdata/seq/A002/A002189.seq | a76b4dd13920b70f10d4097464aa3486 |
A002190 | Sum_{n>=0} a(n)*x^n/n!^2 = -log(BesselJ(0,2*sqrt(x))). | [
"0",
"1",
"1",
"4",
"33",
"456",
"9460",
"274800",
"10643745",
"530052880",
"32995478376",
"2510382661920",
"229195817258100",
"24730000147369440",
"3113066087894608560",
"452168671458789789504",
"75059305956331837485345",
"14121026957032156557396000",
"29886877416946848764956890... | [
"nonn",
"nice"
] | 91 | 0 | 4 | [
"A002190",
"A101981",
"A115368",
"A217940"
] | [
"M3651",
"N1484"
] | N. J. A. Sloane | 2025-11-05T15:21:41 | oeisdata/seq/A002/A002190.seq | 64a8f67d3e3db504380ad81e096a92b6 |
A002191 | Possible values for sum of divisors of n. | [
"1",
"3",
"4",
"6",
"7",
"8",
"12",
"13",
"14",
"15",
"18",
"20",
"24",
"28",
"30",
"31",
"32",
"36",
"38",
"39",
"40",
"42",
"44",
"48",
"54",
"56",
"57",
"60",
"62",
"63",
"68",
"72",
"74",
"78",
"80",
"84",
"90",
"91",
"93",
"96",
"9... | [
"nonn"
] | 67 | 1 | 2 | [
"A000203",
"A002191",
"A007369",
"A007609",
"A054973",
"A083531",
"A175192",
"A211347"
] | [
"M2318",
"N0916"
] | N. J. A. Sloane | 2023-10-14T16:05:00 | oeisdata/seq/A002/A002191.seq | ae31dd4ef4c1075a7556056ffa1922fd |
A002192 | Least integer with A000203(a(n)) = A002191(n), where A002191 = range of the sum-of-divisors function A000203. | [
"1",
"2",
"3",
"5",
"4",
"7",
"6",
"9",
"13",
"8",
"10",
"19",
"14",
"12",
"29",
"16",
"21",
"22",
"37",
"18",
"27",
"20",
"43",
"33",
"34",
"28",
"49",
"24",
"61",
"32",
"67",
"30",
"73",
"45",
"57",
"44",
"40",
"36",
"50",
"42",
"52",... | [
"nonn",
"nice",
"easy"
] | 39 | 1 | 2 | [
"A000203",
"A002191",
"A002192",
"A007609",
"A007626",
"A051444",
"A054973",
"A085790"
] | [
"M0604",
"N0218"
] | N. J. A. Sloane | 2024-12-26T03:52:37 | oeisdata/seq/A002/A002192.seq | 28b107025e0f7b6a52c8bbb974e06200 |
A002193 | Decimal expansion of square root of 2. | [
"1",
"4",
"1",
"4",
"2",
"1",
"3",
"5",
"6",
"2",
"3",
"7",
"3",
"0",
"9",
"5",
"0",
"4",
"8",
"8",
"0",
"1",
"6",
"8",
"8",
"7",
"2",
"4",
"2",
"0",
"9",
"6",
"9",
"8",
"0",
"7",
"8",
"5",
"6",
"9",
"6",
"7",
"1",
"8",
"7",
"... | [
"nonn",
"cons"
] | 286 | 1 | 2 | [
"A001790",
"A002193",
"A004539",
"A005187",
"A010503",
"A014969",
"A020807"
] | [
"M3195",
"N1291"
] | N. J. A. Sloane | 2025-11-05T15:35:24 | oeisdata/seq/A002/A002193.seq | 79c853218cefe6675fd180eeace14a09 |
A002194 | Decimal expansion of sqrt(3). | [
"1",
"7",
"3",
"2",
"0",
"5",
"0",
"8",
"0",
"7",
"5",
"6",
"8",
"8",
"7",
"7",
"2",
"9",
"3",
"5",
"2",
"7",
"4",
"4",
"6",
"3",
"4",
"1",
"5",
"0",
"5",
"8",
"7",
"2",
"3",
"6",
"6",
"9",
"4",
"2",
"8",
"0",
"5",
"2",
"5",
"... | [
"cons",
"nonn",
"easy"
] | 160 | 1 | 2 | [
"A002194",
"A010469",
"A010527",
"A040001",
"A131595",
"A220335"
] | [
"M4326",
"N1812"
] | N. J. A. Sloane | 2025-11-05T15:35:24 | oeisdata/seq/A002/A002194.seq | ed25511b49f05865139e38116903c1a8 |
A002195 | Numerators of coefficients for numerical integration. | [
"1",
"-1",
"11",
"-191",
"2497",
"-14797",
"92427157",
"-36740617",
"61430943169",
"-23133945892303",
"16399688681447",
"-3098811853954483",
"312017413700271173731",
"-69213549869569446541",
"53903636903066465730877",
"-522273861988577772410712439",
"644962185719868974672135609261"
] | [
"sign",
"frac"
] | 59 | 0 | 3 | [
"A000367",
"A002195",
"A002196",
"A006954",
"A008955",
"A009445"
] | [
"M4809",
"N2056"
] | N. J. A. Sloane | 2024-06-01T11:44:34 | oeisdata/seq/A002/A002195.seq | 219c6553ae0244e522ac1051e1a610f1 |
A002196 | Denominators of coefficients for numerical integration. | [
"1",
"12",
"720",
"60480",
"3628800",
"95800320",
"2615348736000",
"4483454976000",
"32011868528640000",
"51090942171709440000",
"152579284313702400000",
"120866571766215475200000",
"50814724101952310083584000000"
] | [
"nonn",
"frac"
] | 47 | 0 | 2 | [
"A000367",
"A002195",
"A002196",
"A006954",
"A008955",
"A009445",
"A160474",
"S1"
] | [
"M4880",
"N2093"
] | N. J. A. Sloane | 2023-06-11T12:12:01 | oeisdata/seq/A002/A002196.seq | a78dbca276dab9df3b7c44476dc28640 |
A002197 | Numerators of coefficients for numerical integration. | [
"1",
"17",
"367",
"27859",
"1295803",
"5329242827",
"25198857127",
"11959712166949",
"11153239773419941",
"31326450596954510807",
"3737565567167418110609",
"2102602044094540855003573",
"189861334343507894443216783"
] | [
"nonn"
] | 51 | 0 | 2 | [
"A000367",
"A002197",
"A002198",
"A002671",
"A006954",
"A008956",
"A160487",
"S1"
] | [
"M5049",
"N2183"
] | N. J. A. Sloane | 2019-03-13T11:33:31 | oeisdata/seq/A002/A002197.seq | 37a8e95194d954159f97ffd3e9827ffe |
A002198 | Denominators of coefficients for numerical integration. | [
"24",
"5760",
"967680",
"464486400",
"122624409600",
"2678117105664000",
"64274810535936000",
"149852129706639360000",
"669659197233029971968000",
"8839501403475995629977600000",
"4879404774718749587747635200000"
] | [
"nonn"
] | 31 | 0 | 1 | [
"A000367",
"A002197",
"A002198",
"A002671",
"A006954",
"A008956",
"A160487",
"S1"
] | [
"M5178",
"N2250"
] | N. J. A. Sloane | 2019-03-13T11:33:36 | oeisdata/seq/A002/A002198.seq | 812dc1d659c6d41d28e5581b5d0912b8 |
A002199 | Least negative primitive root of n-th prime. | [
"1",
"1",
"2",
"2",
"3",
"2",
"3",
"4",
"2",
"2",
"7",
"2",
"6",
"9",
"2",
"2",
"3",
"2",
"4",
"2",
"5",
"2",
"3",
"3",
"5",
"2",
"2",
"3",
"6",
"3",
"9",
"3",
"3",
"4",
"2",
"5",
"5",
"4",
"2",
"2",
"3",
"2",
"2",
"5",
"2",
"... | [
"nonn"
] | 32 | 1 | 3 | [
"A001918",
"A002199",
"A060749"
] | [
"M0245",
"N0085"
] | N. J. A. Sloane | 2024-12-19T05:33:24 | oeisdata/seq/A002/A002199.seq | 7ddf9fd25f1a3193b25cde18989718ca |
A002200 | Primes of the form 2^q*3^r*5^s + 1. | [
"2",
"3",
"5",
"7",
"11",
"13",
"17",
"19",
"31",
"37",
"41",
"61",
"73",
"97",
"101",
"109",
"151",
"163",
"181",
"193",
"241",
"251",
"257",
"271",
"401",
"433",
"487",
"541",
"577",
"601",
"641",
"751",
"769",
"811",
"1153",
"1201",
"1297",
... | [
"nonn"
] | 39 | 1 | 1 | [
"A002200",
"A005109",
"A077497",
"A174144"
] | [
"M0654",
"N0242"
] | N. J. A. Sloane | 2023-10-28T11:24:53 | oeisdata/seq/A002/A002200.seq | 74db7b1350c0263dbb4b71e0e7e75e87 |
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