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timestamp[us]date 1999-12-11 03:00:00
2025-07-19 00:40:46
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|---|---|---|---|---|---|---|---|---|---|---|---|---|
A356501 | Coefficients T(n,k) of x^(4*n+1-k)*y^k in A(x,y) for n >= 0, k = 0..3*n+1, where A(x,y) satisfies: y = Sum_{n=-oo..+oo} (-x)^(n^2) * A(x,y)^((n-1)^2), as an irregular triangle read by rows. | [
"1",
"1",
"0",
"3",
"6",
"4",
"1",
"0",
"9",
"54",
"120",
"135",
"84",
"28",
"4",
"0",
"22",
"294",
"1360",
"3250",
"4662",
"4284",
"2568",
"981",
"219",
"22",
"0",
"51",
"1260",
"10120",
"41405",
"103020",
"170324",
"196172",
"160965",
"94390",
"38896",
"10764",
"1807",
"140",
"0",
"108",
"4590",
"58380",
"368145",
"1404102",
"3587696",
"6515712",
"8715465",
"8763645",
"6684744",
"3863496",
"1670942",
"525980",
"114240",
"15368",
"969"
]
| [
"nonn",
"tabf"
]
| 11 | 0 | 4 | [
"A000716",
"A002293",
"A355872",
"A356500",
"A356501"
]
| null | Paul D. Hanna, Aug 09 2022 | 2022-08-11T07:24:57 | oeisdata/seq/A356/A356501.seq | bf194d15503d237f99ed13454502681b |
A356502 | G.f. A(x) satisfies: 2 = Sum_{n=-oo..+oo} (-x)^(n^2) * A(x)^((n-1)^2). | [
"2",
"17",
"544",
"24344",
"1261702",
"71159152",
"4240009152",
"262584135640",
"16734002688722",
"1090225325371424",
"72285357987696768",
"4861658409827006872",
"330874470176939132844",
"22744684876060771599568",
"1576898258893213475814464",
"110136698483814852518084528",
"7742091796859524187452564262"
]
| [
"nonn"
]
| 11 | 0 | 1 | [
"A354248",
"A356500",
"A356502",
"A356503",
"A356504"
]
| null | Paul D. Hanna, Aug 09 2022 | 2024-01-18T07:31:40 | oeisdata/seq/A356/A356502.seq | 12fc6fb32f5b96aef2cad4910c270343 |
A356503 | G.f. A(x) satisfies: 3 = Sum_{n=-oo..+oo} (-x)^(n^2) * A(x)^((n-1)^2). | [
"3",
"82",
"8856",
"1319544",
"227536218",
"42679033812",
"8455886664768",
"1741107313315440",
"368888770098828828",
"79897573332771325074",
"17610753240158104125072",
"3937441977622780631428392",
"890818276864624495645873656",
"203562312272030478854160019188",
"46914726894168080421554447339136"
]
| [
"nonn"
]
| 10 | 0 | 1 | [
"A354248",
"A356500",
"A356502",
"A356503"
]
| null | Paul D. Hanna, Aug 09 2022 | 2024-01-18T07:33:20 | oeisdata/seq/A356/A356503.seq | 4f22e12211e4e1436e0f48f7a2c5855d |
A356504 | a(n) = A356500(2*n, 2*n+1) for n >= 0. | [
"1",
"4",
"84",
"2568",
"94390",
"3863496",
"169713208",
"7836945872",
"375608185758",
"18527792412380",
"935129979113044",
"48088668037229040",
"2511680568602631894",
"132918633258508425944",
"7113508747197660153120",
"384416086900675623039520",
"20951080869890118976964642"
]
| [
"nonn"
]
| 6 | 0 | 2 | [
"A356500",
"A356504",
"A356505",
"A356506"
]
| null | Paul D. Hanna, Aug 09 2022 | 2022-08-10T07:56:44 | oeisdata/seq/A356/A356504.seq | a886cefe16d016e22211cfab00ece313 |
A356505 | a(n) = A356500(2*n+1, 2*n) for n >= 0. | [
"1",
"6",
"135",
"4284",
"160965",
"6684744",
"296679006",
"13805453160",
"665611197093",
"32988925715610",
"1671463040525586",
"86231285273788180",
"4516133521439246825",
"239551205985729110664",
"12846081444122599438850",
"695428535332816056597520",
"37960416340437631597631877"
]
| [
"nonn"
]
| 6 | 0 | 2 | [
"A356500",
"A356504",
"A356505",
"A356506"
]
| null | Paul D. Hanna, Aug 09 2022 | 2022-08-10T07:56:48 | oeisdata/seq/A356/A356505.seq | 5aa4ab39e02698098171dbb027edc05e |
A356506 | a(n) = A356500(3*n, n+1) for n >= 0. | [
"1",
"6",
"120",
"3250",
"103020",
"3587696",
"133101836",
"5167564380",
"207615129579",
"8567305854998",
"361201849117032",
"15498967122249676",
"674906101555736960",
"29757755664623031984",
"1326196334421645347368",
"59655785739373960058296",
"2705420198806474232850741"
]
| [
"nonn"
]
| 5 | 0 | 2 | [
"A356500",
"A356504",
"A356505",
"A356506"
]
| null | Paul D. Hanna, Aug 09 2022 | 2022-08-10T07:56:52 | oeisdata/seq/A356/A356506.seq | 9566d71478549b4b396c31001022bc79 |
A356507 | G.f.: Sum_{n>=0} x^(n*(n+1)/2) * P(x)^n, where P(x) is the partition function (A000041). | [
"1",
"1",
"1",
"3",
"5",
"10",
"18",
"34",
"60",
"109",
"192",
"339",
"591",
"1027",
"1768",
"3032",
"5165",
"8755",
"14766",
"24786",
"41417",
"68912",
"114193",
"188478",
"309939",
"507821",
"829197",
"1349437",
"2189105",
"3540253",
"5708422",
"9177939",
"14715345",
"23530180",
"37527544",
"59700283",
"94741244",
"149991677"
]
| [
"nonn"
]
| 8 | 0 | 4 | [
"A000041",
"A008485",
"A356507"
]
| null | Paul D. Hanna, Aug 11 2022 | 2022-08-14T15:29:56 | oeisdata/seq/A356/A356507.seq | e96de0b0a71c5ebfbd8a33be721ca965 |
A356508 | G.f. A(x) satisfies: 2 = Product_{n>=1} (1 + x^n*A(x)) * (1 + x^(n-1)/A(x)). | [
"1",
"4",
"14",
"84",
"444",
"2928",
"18214",
"125428",
"844534",
"5989816",
"42186878",
"305757288",
"2215509018",
"16326672796",
"120612763510",
"900561207232",
"6746557569136",
"50906726784700",
"385432963013140",
"2933390906035044",
"22395805754363208",
"171660252748284852",
"1319474586701337644"
]
| [
"nonn"
]
| 17 | 0 | 2 | [
"A000041",
"A052002",
"A356499",
"A356508"
]
| null | Paul D. Hanna, Aug 11 2022 | 2023-09-30T05:24:40 | oeisdata/seq/A356/A356508.seq | 6173e6e8d011e9ef651d52a5c0e18703 |
A356509 | (Negated) Decimal expansion of value of absolute zero in degrees Fahrenheit. | [
"4",
"5",
"9",
"6",
"7"
]
| [
"nonn",
"cons",
"fini",
"full"
]
| 14 | 3 | 1 | [
"A356381",
"A356509"
]
| null | Jianing Song, Aug 11 2022 | 2022-08-11T07:22:53 | oeisdata/seq/A356/A356509.seq | 0e6d717874dbcbcf986571758a98bb3b |
A356510 | Primes p such that 2*p^2 - 7, 2*p^2 - 1, and 2*p^2 + 3 are prime. | [
"43",
"127",
"197",
"3613",
"3767",
"4957",
"28687",
"29723",
"40193",
"46817",
"66403",
"78737",
"89137",
"93253",
"104243",
"105337",
"105673",
"110543",
"114113",
"123397",
"127247",
"145963",
"148303",
"168713",
"173293",
"190387",
"201893",
"207367",
"213613",
"241597",
"256117",
"261323",
"268253",
"278543",
"283807",
"333227",
"339373",
"340913",
"356173",
"359143"
]
| [
"nonn"
]
| 14 | 1 | 1 | [
"A106483",
"A243595",
"A356510"
]
| null | J. M. Bergot and Robert Israel, Aug 09 2022 | 2022-09-05T12:43:16 | oeisdata/seq/A356/A356510.seq | d85c322283934b542fc9899378f66b5b |
A356511 | Total number of distinct numbers that can be obtained by starting with 1 and applying the "Choix de Bruxelles", version 2 operation at most n times in duodecimal (base 12). | [
"1",
"2",
"3",
"4",
"5",
"9",
"19",
"45",
"107",
"275",
"778",
"2581",
"10170",
"45237",
"222859",
"1191214",
"6887258",
"42894933",
"287397837"
]
| [
"nonn",
"more",
"base"
]
| 30 | 0 | 2 | [
"A323289",
"A356511"
]
| null | J. Conrad, Aug 09 2022 | 2025-01-09T13:04:15 | oeisdata/seq/A356/A356511.seq | 5345392db35ce1c83d0b9c2295d0c1d4 |
A356512 | a(n) is the number of tilings of the Aztec diamond of order n using dominoes and square tetrominoes. | [
"1",
"3",
"19",
"293",
"10917",
"996599",
"222222039",
"121552500713",
"162860556763865",
"535527565429290907",
"4318205059450240425083",
"85475498697714319842817853",
"4151186175463797888945512144221"
]
| [
"nonn"
]
| 16 | 0 | 2 | null | null | James Propp, Aug 09 2022 | 2023-04-29T08:11:05 | oeisdata/seq/A356/A356512.seq | aa4ca4587c9b98fdfc3074d8d972f564 |
A356513 | a(n) is the number of tilings of the Aztec diamond of order n using horizontal skew tetrominoes and square tetrominoes. | [
"1",
"1",
"2",
"6",
"40",
"364",
"7904",
"226152",
"15835008",
"1439900880",
"324189571584",
"94080051207136",
"68041472016287744",
"63145927127133361600",
"146637148542938673930240",
"435697213021432661980535936"
]
| [
"nonn"
]
| 16 | 0 | 3 | null | null | James Propp, Aug 09 2022 | 2023-04-29T08:11:01 | oeisdata/seq/A356/A356513.seq | 90c6b3d056cabaeb6da9a3b9ab94c992 |
A356514 | a(n) is the number of tilings of the Aztec diamond of order n using horizontal skew tetrominoes, horizontal straight tetrominoes, and square tetrominoes. | [
"1",
"1",
"2",
"10",
"116",
"3212",
"209152",
"32133552",
"11631456480",
"9922509270288",
"19946786274879008",
"94492874103638971552",
"1054865198752147761744448"
]
| [
"nonn"
]
| 13 | 0 | 3 | null | null | James Propp, Aug 09 2022 | 2023-04-29T08:10:57 | oeisdata/seq/A356/A356514.seq | a6ba51055c4f2276ed6a44b6e0491442 |
A356515 | For any n >= 0, let x_n(1) = n, and for any b > 1, x_n(b) is the sum of digits of x_n(b-1) in base b; x_n is eventually constant, with value a(n). | [
"0",
"1",
"1",
"2",
"1",
"2",
"2",
"1",
"1",
"2",
"2",
"1",
"2",
"1",
"1",
"2",
"1",
"2",
"2",
"1",
"2",
"1",
"1",
"2",
"2",
"1",
"1",
"2",
"1",
"2",
"2",
"3",
"1",
"2",
"2",
"1",
"2",
"1",
"1",
"2",
"2",
"1",
"1",
"2",
"1",
"2",
"2",
"3",
"2",
"1",
"1",
"2",
"1",
"2",
"2",
"3",
"1",
"2",
"2",
"3",
"2",
"3",
"3",
"2",
"1",
"2",
"2",
"1",
"2",
"1",
"1",
"2",
"2",
"1",
"1",
"2",
"1",
"2",
"2",
"3",
"2",
"1",
"1",
"2",
"1",
"2",
"2"
]
| [
"nonn",
"base",
"easy"
]
| 7 | 0 | 4 | [
"A000120",
"A053735",
"A356384",
"A356515",
"A356516"
]
| null | Rémy Sigrist, Aug 09 2022 | 2022-08-12T12:37:31 | oeisdata/seq/A356/A356515.seq | bac0fe326c6ef9f3e77aeff1c56d767c |
A356516 | a(n) is the least k such that A356515(k) = n. | [
"0",
"1",
"3",
"31",
"9007199254740991"
]
| [
"nonn",
"base",
"bref"
]
| 7 | 0 | 3 | [
"A000225",
"A356515",
"A356516",
"A356517"
]
| null | Rémy Sigrist, Aug 10 2022 | 2022-08-12T12:37:26 | oeisdata/seq/A356/A356516.seq | 0ca708300480c6bdd6aae91a90c6bbc3 |
A356517 | Square array A(n, k), n >= 2, k >= 0, read by antidiagonals upwards; A(n, k) is the least integer with sum of digits k in base n. | [
"0",
"0",
"1",
"0",
"1",
"3",
"0",
"1",
"2",
"7",
"0",
"1",
"2",
"5",
"15",
"0",
"1",
"2",
"3",
"8",
"31",
"0",
"1",
"2",
"3",
"7",
"17",
"63",
"0",
"1",
"2",
"3",
"4",
"11",
"26",
"127",
"0",
"1",
"2",
"3",
"4",
"9",
"15",
"53",
"255",
"0",
"1",
"2",
"3",
"4",
"5",
"14",
"31",
"80",
"511",
"0",
"1",
"2",
"3",
"4",
"5",
"11",
"19",
"47",
"161",
"1023",
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"17",
"24",
"63",
"242",
"2047"
]
| [
"nonn",
"tabl",
"base"
]
| 17 | 2 | 6 | [
"A000225",
"A051885",
"A062318",
"A138530",
"A140576",
"A165804",
"A180516",
"A181287",
"A181288",
"A181303",
"A240236",
"A356517"
]
| null | Rémy Sigrist, Aug 10 2022 | 2024-01-05T12:29:30 | oeisdata/seq/A356/A356517.seq | 757934561012b1059b423e8d477f340d |
A356518 | Maximal numerators in approximations to the Aurifeuillian factors of p^p +- 1. | [
"2",
"28",
"1706",
"25082",
"816634",
"157704814"
]
| [
"frac",
"nonn",
"hard",
"more"
]
| 35 | 1 | 1 | [
"A352400",
"A352401",
"A352711",
"A352732",
"A356518",
"A356519"
]
| null | Patrick A. Thomas, Aug 10 2022 | 2022-10-15T20:34:30 | oeisdata/seq/A356/A356518.seq | 30a4db9bbabd8b140e47ab82382f1d9e |
A356519 | Denominators in approximations to the Aurifeuillian factors of p^p +- 1. | [
"3",
"45",
"2835",
"42525",
"1403325",
"273648375"
]
| [
"frac",
"nonn",
"more"
]
| 21 | 1 | 1 | [
"A352400",
"A352401",
"A352711",
"A352732",
"A356518",
"A356519"
]
| null | Patrick A. Thomas, Aug 10 2022 | 2022-10-11T05:14:43 | oeisdata/seq/A356/A356519.seq | 909468dcb4868308c31547b7b14b9da9 |
A356520 | Numbers k such that A000005(A007953(k)) = A007953(k). | [
"1",
"2",
"10",
"11",
"20",
"100",
"101",
"110",
"200",
"1000",
"1001",
"1010",
"1100",
"2000",
"10000",
"10001",
"10010",
"10100",
"11000",
"20000",
"100000",
"100001",
"100010",
"100100",
"101000",
"110000",
"200000",
"1000000",
"1000001",
"1000010",
"1000100",
"1001000",
"1010000",
"1100000",
"2000000",
"10000000",
"10000001"
]
| [
"nonn",
"easy",
"base"
]
| 27 | 1 | 2 | [
"A000005",
"A007953",
"A011557",
"A052216",
"A101318",
"A306509",
"A356061",
"A356520"
]
| null | Ctibor O. Zizka, Aug 10 2022 | 2022-08-24T09:21:26 | oeisdata/seq/A356/A356520.seq | 8b25fdf6411187fc98b60cc0c2e1ef14 |
A356521 | The constant coefficient of (x + x*y + y + 1/(x*y))^n. | [
"1",
"0",
"2",
"6",
"6",
"60",
"110",
"420",
"1750",
"4200",
"19152",
"60060",
"201894",
"792792",
"2525952",
"9525516",
"33886710",
"117738192",
"439904036",
"1544744916",
"5628776296",
"20535629400",
"73621352532",
"270821996016",
"982153129126",
"3583555257360",
"13154522128100",
"47970593626020",
"176337674294760"
]
| [
"nonn"
]
| 44 | 0 | 3 | null | null | Ricardo Acuna, Sep 30 2022 | 2023-12-18T12:47:11 | oeisdata/seq/A356/A356521.seq | a936682fa7ff45e3214a6c2092a6ff3a |
A356522 | Numbers that are nim cubes; numbers in A335170. | [
"0",
"1",
"8",
"10",
"13",
"14",
"16",
"17",
"20",
"21",
"24",
"25",
"30",
"31",
"36",
"38",
"45",
"47",
"49",
"50",
"61",
"62",
"72",
"74",
"76",
"78",
"88",
"90",
"93",
"95",
"105",
"106",
"108",
"111",
"113",
"114",
"117",
"118",
"128",
"130",
"131",
"133",
"136",
"138",
"139",
"141",
"145",
"151",
"152",
"158",
"160",
"161",
"163",
"167",
"169",
"170",
"171",
"173",
"177",
"182",
"186"
]
| [
"nonn"
]
| 9 | 1 | 3 | [
"A051175",
"A335162",
"A335170",
"A335172",
"A356522"
]
| null | Jianing Song, Aug 10 2022 | 2022-08-10T10:07:42 | oeisdata/seq/A356/A356522.seq | 0089a17f85535d377bae4fda490ffb98 |
A356523 | a(n) is the number of tilings of the Aztec diamond of order n using dominoes and horizontal straight tetrominoes. | [
"1",
"2",
"11",
"209",
"12748",
"2432209",
"1473519065",
"2827837404882",
"17158790773744279",
"329479797284568074621",
"20021122370390985464701796",
"3849702362426399132776261664897",
"2342395734889640880082957470488832361"
]
| [
"nonn"
]
| 16 | 0 | 2 | null | null | James Propp, Aug 10 2022 | 2023-04-29T08:10:53 | oeisdata/seq/A356/A356523.seq | de2ca2300a9dce5015d75e3ad7f92a04 |
A356524 | Expansion of e.g.f. Product_{k>0} 1/(1 - k * x^k)^(1/k!). | [
"1",
"1",
"4",
"15",
"100",
"565",
"5946",
"46039",
"605256",
"6646329",
"103614490",
"1320840631",
"27185208876",
"401901829069",
"9042437722878",
"168984439301175",
"4257225193170256",
"85582303577644465",
"2593970612953642386",
"57441717948059605927",
"1862688382990615542900"
]
| [
"nonn"
]
| 13 | 0 | 3 | [
"A006906",
"A209902",
"A294462",
"A354849",
"A356487",
"A356524"
]
| null | Seiichi Manyama, Aug 10 2022 | 2022-08-10T22:34:34 | oeisdata/seq/A356/A356524.seq | 082b00ab3083fb693d5c236b284278c0 |
A356525 | Decimal expansion of number of Pascals (Pa) in 1 millimeter of mercury (mmHg). | [
"1",
"3",
"3",
"3",
"2",
"2",
"3",
"8",
"7",
"4",
"1",
"5"
]
| [
"nonn",
"cons",
"fini",
"full"
]
| 8 | 3 | 2 | [
"A072915",
"A213611",
"A321218",
"A356525",
"A356526",
"A356527",
"H2"
]
| null | Jianing Song, Aug 10 2022 | 2022-08-10T22:35:00 | oeisdata/seq/A356/A356525.seq | ed790c1f0274f222b74999004efe747b |
A356526 | Decimal expansion of number of millimeters of mercury (mmHg) in 1 standard atmosphere (atm). | [
"7",
"5",
"9",
"9",
"9",
"9",
"8",
"9",
"1",
"7",
"2",
"5",
"6",
"1",
"1",
"2",
"8",
"0",
"3",
"7",
"6",
"1",
"2",
"5",
"5",
"6",
"8",
"7",
"9",
"8",
"1",
"9",
"3",
"5",
"7",
"6",
"8",
"1",
"2",
"7",
"9",
"4",
"8",
"8",
"0",
"5",
"9",
"7",
"8",
"8",
"5",
"8",
"1",
"9",
"0",
"7",
"0",
"1",
"1",
"1",
"4",
"9",
"6",
"6",
"2",
"2",
"8",
"7",
"1",
"9",
"6",
"2",
"9",
"9",
"2",
"2",
"9",
"2",
"7",
"7",
"4",
"9",
"4",
"2",
"5",
"7",
"9",
"5",
"8",
"6"
]
| [
"nonn",
"cons"
]
| 8 | 3 | 1 | [
"A213611",
"A321218",
"A356525",
"A356526",
"A356527",
"A356528",
"H2"
]
| null | Jianing Song, Aug 10 2022 | 2022-08-10T22:35:06 | oeisdata/seq/A356/A356526.seq | 2274676e803a2a2c0a4f2283d4e6d7df |
A356527 | Decimal expansion of number of millimeters of water (mmH2O) in 1 millimeter of mercury (mmHg). | [
"1",
"3",
"5",
"9",
"5",
"1"
]
| [
"nonn",
"cons",
"fini",
"full"
]
| 10 | 2 | 2 | [
"A072915",
"A356525",
"A356526",
"A356527",
"A356528",
"H2"
]
| null | Jianing Song, Aug 10 2022 | 2023-07-01T15:24:17 | oeisdata/seq/A356/A356527.seq | 562769c35eeb6f74063aeedfff038fd9 |
A356528 | Decimal expansion of number of millimeters of water (mmH2O) in 1 standard atmosphere (atm). | [
"1",
"0",
"3",
"3",
"2",
"2",
"7",
"4",
"5",
"2",
"7",
"9",
"9",
"8",
"8",
"5",
"7",
"9",
"1",
"7",
"8",
"4",
"1",
"4",
"6",
"4",
"7",
"2",
"0",
"3",
"6",
"8",
"3",
"2",
"1",
"4",
"9",
"6",
"1",
"2",
"7",
"6",
"2",
"7",
"6",
"8",
"1",
"2",
"1",
"6",
"3",
"1",
"7",
"4",
"9",
"8",
"8",
"4",
"0",
"0",
"7",
"2",
"8",
"0",
"7",
"7",
"3",
"7",
"6",
"0",
"6",
"6",
"2",
"4",
"0",
"7",
"6",
"5",
"1",
"9",
"5",
"0",
"4",
"6",
"2",
"1",
"8",
"6",
"3",
"7"
]
| [
"nonn",
"cons",
"easy"
]
| 15 | 5 | 3 | [
"A072915",
"A213611",
"A356526",
"A356527",
"A356528",
"H2"
]
| null | Jianing Song, Aug 10 2022 | 2022-08-13T15:51:09 | oeisdata/seq/A356/A356528.seq | 8224bf3db78fefd11ca2901ffdba8e22 |
A356529 | a(n) = (n-1)! * Sum_{d|n} d^(n-d+1). | [
"1",
"3",
"8",
"78",
"144",
"14400",
"5760",
"5851440",
"88583040",
"5859786240",
"43545600",
"24077414592000",
"6706022400",
"35948640894566400",
"4395744249613516800",
"263312496059348736000",
"376610217984000",
"5901087844517892009984000",
"128047474114560000"
]
| [
"nonn"
]
| 14 | 1 | 2 | [
"A342675",
"A356486",
"A356529",
"A356530"
]
| null | Seiichi Manyama, Aug 10 2022 | 2022-08-10T22:34:39 | oeisdata/seq/A356/A356529.seq | 7faf629419e646d2a77b39e58327536c |
A356530 | Expansion of e.g.f. Product_{k>0} 1/(1 - (k * x)^k)^(1/k^k). | [
"1",
"1",
"4",
"18",
"156",
"1020",
"23040",
"189000",
"8462160",
"174741840",
"8418513600",
"110288455200",
"26670240273600",
"364684824504000",
"46300470369753600",
"5169242034644688000",
"359472799348030368000",
"7508907247291081632000",
"6157317530690533823616000"
]
| [
"nonn"
]
| 11 | 0 | 3 | [
"A023882",
"A294462",
"A356487",
"A356529",
"A356530"
]
| null | Seiichi Manyama, Aug 10 2022 | 2022-08-10T22:34:44 | oeisdata/seq/A356/A356530.seq | e5d9f3cdca5483792c7408b52ad40162 |
A356531 | Primes p == 1 (mod 23) which are norms of elements in the 23rd cyclotomic field. | [
"599",
"691",
"829",
"1151",
"2347",
"2393",
"3037",
"3313",
"3359",
"4463",
"4831",
"5107",
"5521",
"5659",
"6763",
"8741",
"9109",
"9661",
"10627",
"10949",
"11593",
"12743",
"13249",
"14537",
"14767",
"14951",
"15319",
"15733",
"16883",
"17573"
]
| [
"nonn"
]
| 13 | 1 | 1 | null | null | Paul Vanderveen, Aug 10 2022 | 2022-10-02T00:58:29 | oeisdata/seq/A356/A356531.seq | e61a6f5df969c24a2aab5ec858871a3f |
A356532 | Decimal expansion of the Coulomb constant in SI units as defined after 20 May 2019. | [
"8",
"9",
"8",
"7",
"5",
"5",
"1",
"7",
"9"
]
| [
"nonn",
"cons",
"more"
]
| 10 | 10 | 1 | [
"A003673",
"A003676",
"A003678",
"A081823",
"A182999",
"A356532"
]
| null | Jianing Song, Aug 11 2022 | 2022-08-11T14:48:43 | oeisdata/seq/A356/A356532.seq | 0a0bcad9c2f478cef8530411000b41bf |
A356533 | a(n) = sigma_2(n)^2. | [
"1",
"25",
"100",
"441",
"676",
"2500",
"2500",
"7225",
"8281",
"16900",
"14884",
"44100",
"28900",
"62500",
"67600",
"116281",
"84100",
"207025",
"131044",
"298116",
"250000",
"372100",
"280900",
"722500",
"423801",
"722500",
"672400",
"1102500",
"708964",
"1690000",
"925444",
"1863225",
"1488400",
"2102500",
"1690000",
"3651921"
]
| [
"nonn",
"mult"
]
| 17 | 1 | 2 | [
"A001157",
"A035116",
"A072861",
"A127473",
"A356533",
"A356535"
]
| null | Vaclav Kotesovec, Aug 11 2022 | 2023-03-10T10:24:47 | oeisdata/seq/A356/A356533.seq | b5c3761ddf425599dc8faea52167669f |
A356534 | a(n) = sigma_3(n)^2. | [
"1",
"81",
"784",
"5329",
"15876",
"63504",
"118336",
"342225",
"573049",
"1285956",
"1774224",
"4177936",
"4831204",
"9585216",
"12446784",
"21911761",
"24147396",
"46416969",
"47059600",
"84603204",
"92775424",
"143712144",
"148060224",
"268304400",
"248094001",
"391327524",
"417793600",
"630612544",
"594872100"
]
| [
"nonn",
"mult"
]
| 14 | 1 | 2 | [
"A001158",
"A035116",
"A072861",
"A127473",
"A356534",
"A356536"
]
| null | Vaclav Kotesovec, Aug 11 2022 | 2023-03-10T10:26:18 | oeisdata/seq/A356/A356534.seq | 7897c842de42caec19d186d9225c1404 |
A356535 | a(n) = Sum_{k=1..n} sigma_2(k)^2. | [
"1",
"26",
"126",
"567",
"1243",
"3743",
"6243",
"13468",
"21749",
"38649",
"53533",
"97633",
"126533",
"189033",
"256633",
"372914",
"457014",
"664039",
"795083",
"1093199",
"1343199",
"1715299",
"1996199",
"2718699",
"3142500",
"3865000",
"4537400",
"5639900",
"6348864",
"8038864",
"8964308",
"10827533",
"12315933",
"14418433"
]
| [
"nonn"
]
| 13 | 1 | 2 | [
"A001157",
"A035116",
"A057434",
"A061502",
"A072379",
"A072861",
"A127473",
"A356533",
"A356534",
"A356535",
"A356536"
]
| null | Vaclav Kotesovec, Aug 11 2022 | 2022-10-09T04:23:00 | oeisdata/seq/A356/A356535.seq | b79584c348d5a7f9359f1c4335d83e3c |
A356536 | a(n) = Sum_{k=1..n} sigma_3(k)^2. | [
"1",
"82",
"866",
"6195",
"22071",
"85575",
"203911",
"546136",
"1119185",
"2405141",
"4179365",
"8357301",
"13188505",
"22773721",
"35220505",
"57132266",
"81279662",
"127696631",
"174756231",
"259359435",
"352134859",
"495847003",
"643907227",
"912211627",
"1160305628",
"1551633152",
"1969426752",
"2600039296"
]
| [
"nonn"
]
| 20 | 1 | 2 | [
"A001158",
"A035116",
"A057434",
"A061502",
"A072379",
"A072861",
"A127473",
"A356533",
"A356534",
"A356535",
"A356536"
]
| null | Vaclav Kotesovec, Aug 11 2022 | 2023-02-27T16:49:22 | oeisdata/seq/A356/A356536.seq | 41c0d8ece039dd5feba08cf90f16388d |
A356537 | Numbers k whose binary expansion is a substring of the binary expansion of binomial(k,2). | [
"3",
"5",
"9",
"11",
"17",
"33",
"44",
"50",
"58",
"65",
"129",
"257",
"396",
"452",
"513",
"581",
"864",
"971",
"1025",
"1139",
"1843",
"1881",
"1914",
"2049",
"2541",
"2676",
"2929",
"3130",
"4097",
"4596",
"5254",
"6621",
"7010",
"7111",
"8193",
"10771",
"11140",
"12655",
"16385",
"17090",
"19135",
"19371",
"19580",
"20985",
"27117",
"27845",
"32769",
"35272",
"44278",
"46779",
"56069"
]
| [
"nonn",
"base"
]
| 15 | 1 | 1 | [
"A000217",
"A030190",
"A187752",
"A351753",
"A356537"
]
| null | Scott R. Shannon, Aug 11 2022 | 2022-08-11T08:53:46 | oeisdata/seq/A356/A356537.seq | 008e1b3d9a7123da68da5d73887c006d |
A356538 | Expansion of e.g.f. Product_{k>0} 1/(1 - (2 * x)^k)^(1/2^k). | [
"1",
"1",
"5",
"27",
"249",
"2085",
"30645",
"354375",
"6542865",
"108554985",
"2330525925",
"45331607475",
"1288779532425",
"28889867731725",
"876160258298325",
"25315531795929375",
"860642393272286625",
"26527678331237708625",
"1063065483349950205125",
"36393649136002135852875"
]
| [
"nonn"
]
| 11 | 0 | 3 | [
"A000041",
"A006950",
"A090879",
"A356530",
"A356538",
"A356540"
]
| null | Seiichi Manyama, Aug 11 2022 | 2022-08-11T08:54:07 | oeisdata/seq/A356/A356538.seq | ca2b73a2e19149dafdb133f4b9063b32 |
A356539 | a(n) = Sum_{d|n} d * 3^(n-d). | [
"1",
"5",
"12",
"49",
"86",
"492",
"736",
"3977",
"8757",
"34030",
"59060",
"384924",
"531454",
"2672528",
"6672552",
"26093113",
"43046738",
"261646137",
"387420508",
"2181624374",
"4682526672",
"17435870644",
"31381059632",
"204908769276",
"299863458511",
"1412168408630",
"3392641222200",
"13912336721584"
]
| [
"nonn"
]
| 11 | 1 | 2 | [
"A090879",
"A342675",
"A356539",
"A356540"
]
| null | Seiichi Manyama, Aug 11 2022 | 2022-08-11T08:54:12 | oeisdata/seq/A356/A356539.seq | d4345fa883f20ce98de6461d40179cd4 |
A356540 | Expansion of e.g.f. Product_{k>0} 1/(1 - (3 * x)^k)^(1/3^k). | [
"1",
"1",
"6",
"40",
"496",
"5400",
"114400",
"1760080",
"47671680",
"1090230400",
"34312096000",
"916877068800",
"39605683532800",
"1211405062067200",
"55580939301888000",
"2260295506653184000",
"115398744818925568000",
"4928605977341190144000",
"305987190350116667392000"
]
| [
"nonn"
]
| 9 | 0 | 3 | [
"A000041",
"A006950",
"A356530",
"A356538",
"A356539",
"A356540"
]
| null | Seiichi Manyama, Aug 11 2022 | 2022-08-11T08:54:15 | oeisdata/seq/A356/A356540.seq | abaa6b717c4c1787f3a1a93057f644e9 |
A356541 | a(n) = Sum_{d|n} d * (d!)^(n/d-1). | [
"1",
"3",
"4",
"9",
"6",
"33",
"8",
"121",
"118",
"643",
"12",
"7349",
"14",
"35423",
"75904",
"378129",
"18",
"6400179",
"20",
"46256149",
"177951190",
"439086871",
"24",
"21025820825",
"1036800026",
"80951278619",
"1185142088476",
"2117428953117",
"30",
"153033887545887",
"32",
"859169550303265",
"17526860326038562"
]
| [
"nonn"
]
| 13 | 1 | 2 | [
"A356541",
"A356542",
"A356543"
]
| null | Seiichi Manyama, Aug 11 2022 | 2023-08-30T02:00:36 | oeisdata/seq/A356/A356541.seq | f494cad208186f4b324e486c4836fd5b |
A356542 | Expansion of e.g.f. Product_{k>0} 1/(1 - k! * x^k)^(1/k!). | [
"1",
"1",
"4",
"18",
"132",
"900",
"11160",
"100800",
"1809360",
"25053840",
"608428800",
"8610386400",
"469291838400",
"7110609105600",
"404607162960000",
"13958116204032000",
"821937470818464000",
"17420311428103584000",
"2860701872247483264000",
"60029296274562398784000"
]
| [
"nonn"
]
| 8 | 0 | 3 | [
"A209902",
"A356524",
"A356541",
"A356542"
]
| null | Seiichi Manyama, Aug 11 2022 | 2022-08-11T08:54:24 | oeisdata/seq/A356/A356542.seq | 8c8342a52af0eca276ea279b925aa31b |
A356543 | a(n) = Sum_{d|n} (d!)^(n/d-1). | [
"1",
"2",
"2",
"4",
"2",
"12",
"2",
"34",
"38",
"138",
"2",
"1546",
"2",
"5106",
"15698",
"54274",
"2",
"889314",
"2",
"5689090",
"25448258",
"39917826",
"2",
"2486196610",
"207360002",
"6227024898",
"131683574018",
"215393466370",
"2",
"14769495662082",
"2",
"86475697160194",
"1593350982706178",
"355687428161538",
"648227266560002"
]
| [
"nonn"
]
| 13 | 1 | 2 | [
"A087909",
"A342628",
"A356541",
"A356543"
]
| null | Seiichi Manyama, Aug 11 2022 | 2023-08-30T02:00:46 | oeisdata/seq/A356/A356543.seq | fdd4995bacd3c90b7a38f4dffcc08959 |
A356544 | Number of strict closure operators on a set of n elements such that all pairs of nonempty disjoint closed sets can be separated by clopen sets. | [
"0",
"1",
"4",
"35",
"857",
"84230",
"70711467"
]
| [
"nonn",
"hard",
"more"
]
| 51 | 0 | 3 | [
"A334255",
"A356544",
"A358144",
"A358152"
]
| null | Tian Vlasic, Aug 11 2022 | 2024-06-13T11:36:43 | oeisdata/seq/A356/A356544.seq | a4b1149016e1045693e5e2586669a18b |
A356545 | Triangle read by rows. T(n, k) are the coefficients of polynomials p_n(x) based on the Eulerian numbers of first order representing the Bernoulli numbers as B_n = p_n(1) / (n + 1)!. | [
"1",
"1",
"0",
"2",
"-1",
"0",
"6",
"-8",
"2",
"0",
"24",
"-66",
"44",
"-6",
"0",
"120",
"-624",
"792",
"-312",
"24",
"0",
"720",
"-6840",
"14496",
"-10872",
"2736",
"-120",
"0",
"5040",
"-86400",
"285840",
"-347904",
"171504",
"-28800",
"720",
"0",
"40320",
"-1244880",
"6181920",
"-11245680",
"8996544",
"-3090960",
"355680",
"-5040",
"0"
]
| [
"sign",
"tabl"
]
| 41 | 0 | 4 | [
"A027642",
"A098361",
"A123125",
"A129814",
"A164555",
"A173018",
"A356545",
"A356546",
"A356547",
"A356601",
"A356602"
]
| null | Peter Luschny, Aug 11 2022 | 2022-08-15T15:28:46 | oeisdata/seq/A356/A356545.seq | a3784e86db3ea4dd51673e5cf9910fe6 |
A356546 | Triangle read by rows. T(n, k) = RisingFactorial(n + 1, n) / (k! * (n - k)!). | [
"1",
"2",
"2",
"6",
"12",
"6",
"20",
"60",
"60",
"20",
"70",
"280",
"420",
"280",
"70",
"252",
"1260",
"2520",
"2520",
"1260",
"252",
"924",
"5544",
"13860",
"18480",
"13860",
"5544",
"924",
"3432",
"24024",
"72072",
"120120",
"120120",
"72072",
"24024",
"3432",
"12870",
"102960",
"360360",
"720720",
"900900",
"720720",
"360360",
"102960",
"12870"
]
| [
"sign",
"tabl"
]
| 24 | 0 | 2 | [
"A000108",
"A000897",
"A000984",
"A003506",
"A059304",
"A173018",
"A265609",
"A343842",
"A356546"
]
| null | Peter Luschny, Aug 12 2022 | 2023-02-15T04:41:01 | oeisdata/seq/A356/A356546.seq | c6abdb2aa8277f2aa1c30f1a4ab55ed1 |
A356547 | Triangle read by rows. T(n, k) are the coefficients of polynomials p_n(x) based on the Eulerian numbers of second order representing the Bernoulli numbers as B_n = p_n(1) / (2*(2*n - 1)!). | [
"1",
"1",
"0",
"6",
"-4",
"0",
"120",
"-192",
"72",
"0",
"5040",
"-15840",
"13920",
"-3456",
"0",
"362880",
"-2096640",
"3306240",
"-1918080",
"345600",
"0",
"39916800",
"-413683200",
"1053803520",
"-1064448000",
"448519680",
"-62208000",
"0",
"6227020800",
"-114960384000",
"447866496000",
"-699342336000",
"506348236800",
"-164428185600",
"18289152000",
"0"
]
| [
"sign",
"tabl"
]
| 17 | 0 | 4 | [
"A027642",
"A164555",
"A201637",
"A356545",
"A356547"
]
| null | Peter Luschny, Aug 12 2022 | 2023-03-18T08:49:14 | oeisdata/seq/A356/A356547.seq | 87719dde0ad64a452fa169704a2b8ff7 |
A356548 | Let S(n)=sigma(n)/3. Numbers k such that S^m(k)=k, 1/3-sociable numbers (of any order). | [
"120",
"672",
"7560",
"7680",
"8064",
"8184",
"8840",
"9600",
"10540",
"34944",
"36576",
"38080",
"65520",
"71680",
"75264",
"77748",
"90272",
"472416",
"510720",
"523776",
"605024",
"654080",
"1100190",
"1124352",
"14913024",
"16149760",
"27797760",
"33931072",
"34012160",
"459818240"
]
| [
"nonn",
"more"
]
| 16 | 1 | 1 | [
"A005820",
"A113546",
"A356548"
]
| null | Michel Marcus, Aug 11 2022 | 2022-08-14T06:53:16 | oeisdata/seq/A356/A356548.seq | 6000a6834556156186aa13735aa5a0e1 |
A356549 | a(n) is the number of divisors of 10^n whose first digit is 1. | [
"1",
"2",
"3",
"5",
"8",
"11",
"15",
"20",
"25",
"31",
"38",
"45",
"52",
"60",
"69",
"78",
"88",
"99",
"110",
"122",
"135",
"148",
"161",
"175",
"190",
"205",
"221",
"238",
"255",
"273",
"292",
"311",
"330",
"350",
"371",
"392",
"414",
"437",
"460",
"484",
"509",
"534",
"559",
"585",
"612",
"639",
"667",
"696",
"725",
"755",
"786",
"817",
"848",
"880",
"913",
"946",
"980",
"1015",
"1050",
"1086"
]
| [
"nonn",
"base"
]
| 46 | 0 | 2 | [
"A011557",
"A356549",
"A357299"
]
| null | Michel Marcus, Sep 23 2022 | 2022-09-24T01:43:29 | oeisdata/seq/A356/A356549.seq | 20ec142143cfe75e6b1236f50d509731 |
A356550 | a(n) is the period of {F(F(k)) mod n, k >= 0}, where F denotes the Fibonacci numbers (A000045). | [
"1",
"4",
"12",
"24",
"60",
"12",
"24",
"24",
"24",
"60",
"60",
"24",
"48",
"24",
"60",
"24",
"24",
"24",
"24",
"120",
"24",
"60",
"24",
"24",
"300",
"48",
"24",
"24",
"48",
"60",
"120",
"24",
"60",
"24",
"120",
"24",
"18",
"24",
"48",
"120",
"60",
"24",
"60",
"120",
"120",
"24",
"48",
"24",
"48",
"300",
"24",
"48",
"72",
"24",
"60",
"24",
"24",
"48",
"42",
"120",
"120",
"120",
"24"
]
| [
"nonn"
]
| 5 | 1 | 2 | [
"A000045",
"A001175",
"A007570",
"A356550"
]
| null | Rémy Sigrist, Aug 11 2022 | 2022-08-15T05:19:56 | oeisdata/seq/A356/A356550.seq | c36d3e32ef094299fba3f36129bdcb98 |
A356551 | a(n) = A005132(n+2) - A005132(n). | [
"3",
"5",
"-1",
"1",
"11",
"13",
"-1",
"1",
"-1",
"1",
"-1",
"1",
"-1",
"1",
"-1",
"1",
"35",
"37",
"-1",
"1",
"-1",
"-45",
"1",
"-1",
"1",
"-1",
"1",
"-1",
"1",
"-1",
"1",
"65",
"67",
"-1",
"1",
"-1",
"-75",
"1",
"-1",
"1",
"-1",
"1",
"-1",
"1",
"-1",
"1",
"-1",
"1",
"-1",
"1",
"-1",
"1",
"-1",
"1",
"-1",
"1",
"-1",
"1",
"-1",
"1",
"-1",
"1",
"-1",
"1",
"131",
"133",
"-1",
"1",
"-1"
]
| [
"sign"
]
| 50 | 0 | 1 | [
"A005132",
"A160356",
"A356551"
]
| null | Paul Curtz, Aug 12 2022 | 2022-09-16T02:13:54 | oeisdata/seq/A356/A356551.seq | 994a32a429148d5136dd0b96c84c403e |
A356552 | a(n) is the least base b > 1 where the sum of digits of n divides n. | [
"2",
"2",
"3",
"2",
"5",
"2",
"7",
"2",
"3",
"2",
"11",
"2",
"13",
"7",
"3",
"2",
"17",
"2",
"19",
"2",
"2",
"11",
"23",
"2",
"3",
"5",
"3",
"3",
"29",
"3",
"31",
"2",
"3",
"2",
"3",
"2",
"37",
"19",
"3",
"2",
"41",
"2",
"43",
"6",
"3",
"23",
"47",
"2",
"7",
"4",
"5",
"4",
"53",
"3",
"2",
"3",
"3",
"29",
"59",
"2",
"61",
"31",
"3",
"2",
"3",
"2",
"67",
"2",
"2",
"6",
"71",
"2",
"73",
"37",
"3",
"4",
"3",
"3",
"79"
]
| [
"nonn",
"base"
]
| 11 | 1 | 1 | [
"A049445",
"A356552",
"A356553"
]
| null | Rémy Sigrist, Aug 12 2022 | 2022-09-19T07:23:24 | oeisdata/seq/A356/A356552.seq | da2229bf4f9266135394a66fe462596b |
A356553 | For any n > 0, let b > 1 be the least base where the sum of digits of n divides n; a(n) is the sum of digits of n in base b. | [
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"2",
"3",
"1",
"1",
"2",
"1",
"2",
"3",
"2",
"1",
"2",
"5",
"2",
"1",
"2",
"1",
"2",
"1",
"1",
"3",
"2",
"5",
"2",
"1",
"2",
"3",
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"1",
"4",
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"1",
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"3",
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"1",
"2",
"5",
"4",
"3",
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"1",
"4",
"1",
"2",
"3",
"1",
"5",
"2",
"1",
"2",
"3",
"10",
"1",
"2",
"1",
"2",
"5",
"4",
"7",
"6",
"1",
"2",
"3",
"2",
"1",
"3",
"5",
"2",
"3"
]
| [
"nonn",
"base"
]
| 9 | 1 | 6 | [
"A356552",
"A356553"
]
| null | Rémy Sigrist, Aug 12 2022 | 2022-09-19T07:23:21 | oeisdata/seq/A356/A356553.seq | d7e2a9f575a57d5913fa7bec772e33cf |
A356554 | Expansion of e.g.f. ( Product_{k>0} 1/(1-x^k)^k )^x. | [
"1",
"0",
"2",
"15",
"92",
"930",
"8514",
"116760",
"1445744",
"23020200",
"373858920",
"6756785640",
"130982295432",
"2751191997840",
"61046788571664",
"1445520760702200",
"36387213668348160",
"960383111961228480",
"26780931923301572544",
"781864626481646405760",
"23925584882896903854720"
]
| [
"nonn"
]
| 19 | 0 | 3 | [
"A001157",
"A066166",
"A354623",
"A355064",
"A356337",
"A356554",
"A356566"
]
| null | Seiichi Manyama, Aug 12 2022 | 2022-08-13T11:27:50 | oeisdata/seq/A356/A356554.seq | cd35804297dc5c078af9ff1f7c2bda5c |
A356555 | Irregular triangle T(n, k), n > 0, k = 1..A080221(n) read by rows; the n-th row contains, in ascending order, the bases b from 2..n+1 where the sum of digits of n divides n. | [
"2",
"2",
"3",
"3",
"4",
"2",
"3",
"4",
"5",
"5",
"6",
"2",
"3",
"4",
"5",
"6",
"7",
"7",
"8",
"2",
"3",
"4",
"5",
"7",
"8",
"9",
"3",
"4",
"7",
"9",
"10",
"2",
"3",
"5",
"6",
"9",
"10",
"11",
"11",
"12",
"2",
"3",
"4",
"5",
"6",
"7",
"9",
"10",
"11",
"12",
"13",
"13",
"14",
"7",
"8",
"13",
"14",
"15",
"3",
"5",
"6",
"7",
"11",
"13",
"15",
"16",
"2",
"3",
"4",
"5",
"7",
"8",
"9",
"13",
"15",
"16",
"17",
"17",
"18"
]
| [
"nonn",
"base",
"tabf"
]
| 10 | 1 | 1 | [
"A080221",
"A356552",
"A356555"
]
| null | Rémy Sigrist, Aug 12 2022 | 2022-08-15T05:22:59 | oeisdata/seq/A356/A356555.seq | 83f2b86bc896418f57c18fbae1a52a42 |
A356556 | Parity of A061418. | [
"0",
"1",
"0",
"0",
"1",
"1",
"1",
"0",
"0",
"1",
"0",
"1",
"1",
"0",
"0",
"1",
"0",
"1",
"0",
"1",
"1",
"0",
"0",
"1",
"0",
"1",
"1",
"0",
"1",
"0",
"1",
"1",
"1",
"1",
"1",
"0",
"0",
"1",
"0",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"1",
"1",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"1",
"0",
"1",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"1",
"1",
"1",
"1",
"1",
"0",
"0",
"1",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"1",
"1",
"0",
"1",
"1",
"0"
]
| [
"easy",
"nonn"
]
| 27 | 1 | null | [
"A061418",
"A356556"
]
| null | Jacob Fauman, Aug 12 2022 | 2022-12-26T11:39:27 | oeisdata/seq/A356/A356556.seq | 7274d81c6b99f631c4cab0fcdd1995ce |
A356557 | Start with a(1)=2; to get a(n+1) insert in a(n) at the rightmost possible position the smallest possible digit such that the new number is a prime. | [
"2",
"23",
"233",
"2333",
"23333",
"233323",
"2333231",
"23332301",
"233323001",
"2333230019",
"23332030019",
"233320360019",
"2333203600159",
"23332036001959",
"233320360019569",
"2333203600195669",
"23332036001956469",
"233320360019564269",
"2333203600195642469",
"23332036001956424629",
"233320360019564246269"
]
| [
"nonn",
"base"
]
| 49 | 1 | 1 | [
"A125001",
"A332603",
"A356557",
"A357436"
]
| null | Bartlomiej Pawlik, Aug 12 2022 | 2023-06-12T12:33:09 | oeisdata/seq/A356/A356557.seq | 917bbdaeffbd8789d8a2772ea8253ac6 |
A356558 | Triangle read by rows: T(n,k), where n, k >= 2, is the number of n-element unlabeled connected series-parallel posets with k ordinal terms that are either the singleton or disconnected posets. | [
"1",
"2",
"1",
"5",
"3",
"1",
"16",
"9",
"4",
"1",
"52",
"31",
"14",
"5",
"1",
"188",
"108",
"52",
"20",
"6",
"1",
"690",
"402",
"193",
"80",
"27",
"7",
"1",
"2638",
"1523",
"744",
"315",
"116",
"35",
"8",
"1",
"10272",
"5934",
"2908",
"1261",
"483",
"161",
"44",
"9",
"1",
"40782",
"23505",
"11580",
"5085",
"2010",
"707",
"216",
"54",
"10",
"1"
]
| [
"nonn",
"tabl",
"more"
]
| 13 | 2 | 2 | [
"A007453",
"A263864",
"A349488",
"A356558"
]
| null | Salah Uddin Mohammad, Aug 12 2022 | 2022-10-05T04:46:37 | oeisdata/seq/A356/A356558.seq | 919fa5affb5471327b42401103898220 |
A356559 | a(n) = exp(-1) * n! * Sum_{k>=0} Laguerre(n,k) / k!. | [
"1",
"0",
"0",
"1",
"7",
"43",
"281",
"2056",
"17004",
"157809",
"1622515",
"18245335",
"222004597",
"2898508416",
"40343356184",
"595578837205",
"9287308741827",
"152459628788599",
"2627373030049669",
"47425289731038656",
"895098852673047772",
"17644305594671247141",
"363065584549610882703",
"7799894520723959486795"
]
| [
"nonn"
]
| 8 | 0 | 5 | [
"A000110",
"A009940",
"A101053",
"A317362",
"A317366",
"A356559"
]
| null | Ilya Gutkovskiy, Aug 12 2022 | 2025-02-16T08:34:03 | oeisdata/seq/A356/A356559.seq | 159cf72edee79cd7983e48191aaadd86 |
A356560 | Expansion of e.g.f. Product_{k>0} 1/(1 - k^2 * x^k)^(1/k^2). | [
"1",
"1",
"4",
"18",
"156",
"1020",
"16560",
"143640",
"2898000",
"43016400",
"926856000",
"13749674400",
"524416939200",
"8626888670400",
"284030505158400",
"7950850859952000",
"284397434953632000",
"6752059834744224000",
"357295791069689472000",
"9098085523917918528000"
]
| [
"nonn"
]
| 13 | 0 | 3 | [
"A077335",
"A294462",
"A294469",
"A308688",
"A356530",
"A356560",
"A356561"
]
| null | Seiichi Manyama, Aug 12 2022 | 2022-08-12T09:21:18 | oeisdata/seq/A356/A356560.seq | 90e9dedf63060383dc79a892e01bf282 |
A356561 | Expansion of e.g.f. Product_{k>0} 1/(1 - k^3 * x^k)^(1/k^3). | [
"1",
"1",
"4",
"18",
"204",
"1260",
"37440",
"299880",
"11002320",
"204860880",
"6618628800",
"92924647200",
"8181137764800",
"124123075876800",
"7211104918617600",
"288085376346768000",
"14964000305173920000",
"340302035937191328000",
"42619767305209750656000"
]
| [
"nonn"
]
| 10 | 0 | 3 | [
"A265837",
"A294462",
"A294469",
"A308689",
"A356530",
"A356560",
"A356561"
]
| null | Seiichi Manyama, Aug 12 2022 | 2022-08-12T09:21:13 | oeisdata/seq/A356/A356561.seq | cdc598ba119489cb604c47c229f4ff43 |
A356562 | Decimal expansion of the unique positive real root of the equation x^x^x = x^x + 1. | [
"1",
"6",
"7",
"1",
"2",
"9",
"2",
"1",
"9",
"7",
"9",
"8",
"8",
"9",
"3",
"2",
"5",
"5",
"2",
"8",
"0",
"2",
"2",
"2",
"4",
"6",
"3",
"4",
"1",
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"1",
"4",
"6",
"1",
"1",
"1",
"1",
"2",
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"4",
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"0",
"4",
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"2",
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"3",
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"2",
"3",
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"8",
"0",
"3",
"3",
"7",
"1",
"7",
"7",
"3",
"9",
"6",
"0",
"2",
"3",
"3",
"6",
"4",
"9",
"0",
"6",
"4",
"2",
"6",
"9"
]
| [
"cons",
"nonn"
]
| 33 | 1 | 2 | [
"A073229",
"A124930",
"A356562"
]
| null | Marco Ripà, Aug 12 2022 | 2022-08-22T22:16:14 | oeisdata/seq/A356/A356562.seq | 50dec69a7df8d5bded08767dbbf96d62 |
A356563 | Sums of powers of roots of x^3 - 2*x^2 - x - 2. | [
"3",
"2",
"6",
"20",
"50",
"132",
"354",
"940",
"2498",
"6644",
"17666",
"46972",
"124898",
"332100",
"883042",
"2347980",
"6243202",
"16600468",
"44140098",
"117367068",
"312075170",
"829797604",
"2206404514",
"5866756972",
"15599513666",
"41478593332",
"110290214274"
]
| [
"nonn",
"easy"
]
| 10 | 0 | 1 | [
"A077996",
"A348909",
"A356563"
]
| null | Greg Dresden and Hanzhang Fang, Aug 12 2022 | 2022-08-13T06:24:46 | oeisdata/seq/A356/A356563.seq | eb98b80e3ae09b2ca96b60045c6dbcf9 |
A356564 | Expansion of e.g.f. ( Product_{k>0} (1+x^k)^(1/k) )^x. | [
"1",
"0",
"2",
"0",
"28",
"-30",
"888",
"-1260",
"51728",
"-196560",
"5293080",
"-22286880",
"710229408",
"-4851269280",
"138348035616",
"-1091188098000",
"36482139114240",
"-379928382462720",
"11812558481332992",
"-137793570801143040",
"4609972759421554560",
"-67292912045817561600"
]
| [
"sign"
]
| 13 | 0 | 3 | [
"A007113",
"A048272",
"A338814",
"A356392",
"A356564",
"A356565",
"A356566"
]
| null | Seiichi Manyama, Aug 12 2022 | 2022-08-13T11:28:05 | oeisdata/seq/A356/A356564.seq | c028c3308916c14528290813065db50f |
A356565 | Expansion of e.g.f. ( Product_{k>0} (1+x^k) )^x. | [
"1",
"0",
"2",
"3",
"44",
"90",
"2034",
"9240",
"168944",
"951048",
"24042600",
"185387400",
"4411634952",
"44020650960",
"1166597641104",
"14101322278680",
"399099955203840",
"5522583764698560",
"169123038510919104",
"2779010889700890240",
"87888034148774728320",
"1637061268780618450560"
]
| [
"nonn"
]
| 15 | 0 | 3 | [
"A000593",
"A007113",
"A356393",
"A356564",
"A356565",
"A356566"
]
| null | Seiichi Manyama, Aug 12 2022 | 2022-08-17T02:35:14 | oeisdata/seq/A356/A356565.seq | c49a016469aaa45ac613d99c807802b3 |
A356566 | Expansion of e.g.f. ( Product_{k>0} (1+x^k)^k )^x. | [
"1",
"0",
"2",
"9",
"92",
"510",
"7074",
"68040",
"1002224",
"12529944",
"228706920",
"3565888920",
"71035245192",
"1348127454960",
"30270949077264",
"661700017709640",
"16516072112482560",
"408336559236083520",
"11204399270843020224",
"309489391954850336640",
"9258803420755891835520"
]
| [
"nonn"
]
| 14 | 0 | 3 | [
"A007113",
"A078306",
"A356394",
"A356564",
"A356565",
"A356566"
]
| null | Seiichi Manyama, Aug 12 2022 | 2022-08-13T11:28:30 | oeisdata/seq/A356/A356566.seq | 6a9fd575d2ed57c061aeb43afc244e55 |
A356567 | Numbers that generate increasing numbers of consecutive primes when doubled and added to the sequence of odd squares. (Positions of records in A354499.) | [
"1",
"2",
"11",
"29",
"326"
]
| [
"nonn",
"more"
]
| 38 | 1 | 2 | [
"A016754",
"A145202",
"A188459",
"A354499",
"A356567"
]
| null | Steven M. Altschuld, Aug 12 2022 | 2022-10-05T04:52:39 | oeisdata/seq/A356/A356567.seq | 2d4797cec12f5319a13870a58c5929cd |
A356568 | a(n) = (4^n - 1)*n^(2*n). | [
"0",
"3",
"240",
"45927",
"16711680",
"9990234375",
"8913923665920",
"11111328602485167",
"18446462598732840960",
"39346257980661240576303",
"104857500000000000000000000",
"341427795961470170556885610263",
"1333735697353436921058237339402240",
"6156119488473827117528057630000587767"
]
| [
"nonn",
"easy"
]
| 55 | 0 | 2 | [
"A062206",
"A085534",
"A356568"
]
| null | Enrique Navarrete, Sep 30 2022 | 2025-03-09T10:30:47 | oeisdata/seq/A356/A356568.seq | c14350e7bfb67553ad0008a48e084ca5 |
A356569 | Sums of powers of roots of x^4 - 2*x^3 - 6*x^2 + 2*x + 1. | [
"4",
"2",
"16",
"38",
"164",
"522",
"1936",
"6638",
"23684",
"82802",
"292496",
"1027798",
"3621284",
"12741562",
"44862736",
"157904478",
"555880964",
"1956721762",
"6888057616",
"24246779398",
"85352580004",
"300452999402",
"1057639862416"
]
| [
"nonn",
"easy"
]
| 17 | 0 | 1 | [
"A158934",
"A192380",
"A356569"
]
| null | Greg Dresden and Ding Hao, Aug 12 2022 | 2022-08-15T10:27:33 | oeisdata/seq/A356/A356569.seq | 0524a37f9733c2080e9483d81e56a5a3 |
A356570 | a(n) is the first prime that starts a sequence of exactly n consecutive primes that are in A048519. | [
"19",
"11",
"97",
"72461",
"346373",
"2587093",
"1534359019",
"1010782220887"
]
| [
"nonn",
"base",
"more"
]
| 11 | 1 | 1 | [
"A048519",
"A356570"
]
| null | J. M. Bergot and Robert Israel, Aug 12 2022 | 2022-09-04T12:52:16 | oeisdata/seq/A356/A356570.seq | 6ed7157487d81f1f354daedb30a41176 |
A356571 | a(n) = floor(f(n)), where f(n) = n^4*(15-24*n+10*n^2) + 20*n^5*(1-n)^3 / (1-2*n(1-n)). | [
"0",
"1",
"-16",
"-318",
"-1895",
"-6936",
"-19313",
"-45055",
"-92831",
"-174433",
"-305249",
"-504751",
"-796967",
"-1210969",
"-1781345",
"-2548687",
"-3560063",
"-4869505",
"-6538481",
"-8636383",
"-11240999",
"-14439001",
"-18326417",
"-23009119",
"-28603295",
"-35235937",
"-43045313",
"-52181455",
"-62806631",
"-75095833",
"-89237249"
]
| [
"sign"
]
| 35 | 0 | 3 | null | null | Christoph B. Kassir, Aug 12 2022 | 2022-10-05T05:05:51 | oeisdata/seq/A356/A356571.seq | 43776d1c37a694d546e172081d532266 |
A356572 | Expansion of e.g.f. sinh( (exp(3*x) - 1)/3 ). | [
"0",
"1",
"3",
"10",
"45",
"307",
"2718",
"26371",
"265359",
"2778976",
"30916863",
"372113623",
"4873075056",
"68908186765",
"1037694932823",
"16438615126282",
"271972422548361",
"4687666317874495",
"84181305836224422",
"1576083180118379527",
"30757003280682603699",
"624671260245315540568"
]
| [
"nonn"
]
| 33 | 0 | 3 | [
"A009599",
"A024429",
"A356572",
"A357617",
"A357649"
]
| null | Seiichi Manyama, Oct 07 2022 | 2022-10-07T15:47:07 | oeisdata/seq/A356/A356572.seq | 1b135aff4858d4b899daff5a0c187ecb |
A356573 | Sigma-dense numbers: integers k such that sigma(k) * log(1+log(1+log(1+k))) / (k * log(1+log(1+k))) sets a new record. | [
"1",
"2",
"4",
"6",
"12",
"24",
"60",
"120",
"240",
"360",
"720",
"840",
"1260",
"1680",
"2520",
"5040",
"10080",
"15120",
"27720",
"55440",
"110880",
"166320",
"277200",
"332640",
"554400",
"720720",
"1441440",
"2162160",
"3603600",
"4324320",
"7207200",
"10810800",
"21621600",
"36756720",
"61261200",
"73513440",
"122522400",
"183783600"
]
| [
"nonn"
]
| 70 | 1 | 2 | [
"A000005",
"A000203",
"A210594",
"A356573"
]
| null | Hal M. Switkay, Dec 11 2022 | 2022-12-12T09:38:41 | oeisdata/seq/A356/A356573.seq | da16fd57576d6b2bce5dfd67ca47ddc6 |
A356574 | a(n) = Sum_{d|n} tau(d^4), where tau(n) = number of divisors of n, cf. A000005. | [
"1",
"6",
"6",
"15",
"6",
"36",
"6",
"28",
"15",
"36",
"6",
"90",
"6",
"36",
"36",
"45",
"6",
"90",
"6",
"90",
"36",
"36",
"6",
"168",
"15",
"36",
"28",
"90",
"6",
"216",
"6",
"66",
"36",
"36",
"36",
"225",
"6",
"36",
"36",
"168",
"6",
"216",
"6",
"90",
"90",
"36",
"6",
"270",
"15",
"90",
"36",
"90",
"6",
"168",
"36",
"168",
"36",
"36",
"6",
"540",
"6",
"36",
"90",
"91",
"36",
"216",
"6",
"90",
"36",
"216",
"6",
"420",
"6",
"36",
"90",
"90"
]
| [
"nonn",
"easy",
"mult"
]
| 63 | 1 | 2 | [
"A000005",
"A007425",
"A035116",
"A061391",
"A321348",
"A356574",
"A358380",
"A359037",
"A359038"
]
| null | Seiichi Manyama, Dec 13 2022 | 2022-12-15T09:59:49 | oeisdata/seq/A356/A356574.seq | 24364c64811a4619dfebd72c3f309837 |
A356575 | Expansion of e.g.f. ( Product_{k>0} 1/(1-x^k)^(1/k!) )^x. | [
"1",
"0",
"2",
"6",
"24",
"185",
"990",
"9877",
"72968",
"824553",
"8495560",
"102689741",
"1317098772",
"18729163609",
"270642677396",
"4396374315075",
"73997950572016",
"1318896555293137",
"24900891903482832",
"499312682762581945",
"10301544926241347140",
"227464062944112566481"
]
| [
"nonn"
]
| 16 | 0 | 3 | [
"A087906",
"A356025",
"A356575",
"A356576"
]
| null | Seiichi Manyama, Aug 12 2022 | 2022-08-13T11:29:02 | oeisdata/seq/A356/A356575.seq | 5356187dbea38ccf65ad594f1867cf17 |
A356576 | Expansion of e.g.f. ( Product_{k>0} (1+x^k)^(1/k!) )^x. | [
"1",
"0",
"2",
"0",
"24",
"-55",
"630",
"-2723",
"30968",
"-294327",
"3047320",
"-30255379",
"387690732",
"-5565964391",
"77090414492",
"-1114263777885",
"18473122449616",
"-331776991760303",
"6106973926830192",
"-112710455017397639",
"2233663985151902860",
"-50049383051597936559"
]
| [
"sign"
]
| 13 | 0 | 3 | [
"A352013",
"A356402",
"A356575",
"A356576"
]
| null | Seiichi Manyama, Aug 12 2022 | 2022-08-13T11:29:48 | oeisdata/seq/A356/A356576.seq | 50f31ff9602189b2072cb0dce5b40d18 |
A356577 | Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k/k) )^x. | [
"1",
"0",
"2",
"6",
"28",
"195",
"1248",
"11200",
"97088",
"1036602",
"11477230",
"142038996",
"1883459928",
"27044341896",
"412487825540",
"6745633845210",
"116679466051968",
"2137078798914128",
"41252266236703320",
"838320793571448408",
"17846205347898263960",
"398262850748807921856"
]
| [
"nonn"
]
| 11 | 0 | 3 | [
"A308345",
"A356408",
"A356577"
]
| null | Seiichi Manyama, Aug 12 2022 | 2022-08-13T11:29:30 | oeisdata/seq/A356/A356577.seq | f4b8665a8c97625936fa5aae7f103574 |
A356578 | Expansion of e.g.f. ( Product_{k>0} 1/(1 - k * x^k) )^x. | [
"1",
"0",
"2",
"15",
"92",
"1050",
"8514",
"147000",
"1546544",
"29673000",
"478186920",
"9011752200",
"178483287432",
"4205087686800",
"91775320005264",
"2290742704668600",
"63289842765692160",
"1696665419122968000",
"50287699532618564544",
"1549916411848463721600"
]
| [
"nonn"
]
| 12 | 0 | 3 | [
"A078308",
"A353993",
"A354848",
"A356578"
]
| null | Seiichi Manyama, Aug 12 2022 | 2022-08-13T11:29:17 | oeisdata/seq/A356/A356578.seq | 0abe4c6b3ed5236d0f18b41bbfcaa811 |
A356579 | Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k/k!) )^x. | [
"1",
"0",
"2",
"6",
"24",
"170",
"990",
"8267",
"67928",
"661698",
"6923010",
"78997457",
"983728812",
"13101433501",
"187893745130",
"2869108871085",
"46643882262448",
"803224515183482",
"14618310020427402",
"280340253237270977",
"5651276469430635620",
"119483759770082806035",
"2644015844432596590946"
]
| [
"nonn"
]
| 9 | 0 | 3 | [
"A182926",
"A356409",
"A356579"
]
| null | Seiichi Manyama, Aug 12 2022 | 2022-08-13T11:28:42 | oeisdata/seq/A356/A356579.seq | 8f9b2fc2158e643535220906e749ffd5 |
A356580 | Decimal expansion of log(2) - gamma - 1/2 (negated). | [
"3",
"8",
"4",
"0",
"6",
"8",
"4",
"8",
"4",
"3",
"4",
"1",
"5",
"8",
"7",
"5",
"5",
"1",
"1",
"8",
"9",
"2",
"7",
"9",
"9",
"6",
"8",
"6",
"2",
"4",
"2",
"2",
"5",
"8",
"6",
"2",
"9",
"6",
"6",
"6",
"5",
"9",
"2",
"0",
"1",
"5",
"7",
"9",
"6",
"6",
"8",
"3",
"4",
"4",
"6",
"8",
"5",
"0",
"8",
"7",
"2",
"2",
"5",
"3",
"9",
"1",
"4",
"7",
"4",
"1",
"0",
"4",
"8",
"0",
"7",
"9",
"6",
"9",
"9",
"5",
"5",
"3",
"3",
"1",
"0",
"8",
"3",
"7",
"3",
"6",
"2",
"9",
"5",
"3",
"2",
"8",
"0",
"6",
"1",
"9",
"7",
"2",
"6",
"2",
"9"
]
| [
"nonn",
"cons"
]
| 9 | 0 | 1 | [
"A001620",
"A002162",
"A356580",
"A356581"
]
| null | Amiram Eldar, Aug 13 2022 | 2022-08-13T10:08:04 | oeisdata/seq/A356/A356580.seq | c85bae85a0f96cf25e1fbeca29ea28b3 |
A356581 | Decimal expansion of gamma - 3*log(2) + log(3) + 17/24. | [
"3",
"0",
"4",
"7",
"1",
"9",
"7",
"4",
"5",
"2",
"2",
"3",
"1",
"3",
"9",
"9",
"5",
"7",
"0",
"8",
"3",
"3",
"9",
"4",
"2",
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"5",
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"3",
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"2",
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"5",
"1",
"1",
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"5",
"4",
"8",
"7",
"3",
"3",
"7",
"5",
"5",
"1",
"4",
"4",
"8",
"7",
"4",
"2",
"0",
"5",
"2",
"2",
"8",
"2",
"4",
"3",
"2",
"6",
"3",
"0",
"6",
"1",
"7",
"0",
"4",
"4",
"9",
"5",
"5",
"6",
"1",
"0",
"9",
"0",
"0",
"9",
"9",
"3",
"0"
]
| [
"nonn",
"cons"
]
| 7 | 0 | 1 | [
"A001620",
"A002162",
"A002391",
"A356580",
"A356581"
]
| null | Amiram Eldar, Aug 13 2022 | 2022-08-14T03:43:38 | oeisdata/seq/A356/A356581.seq | 0b35dae9367f4f1cd35f3e0bd83eb0b1 |
A356582 | T(n,k) is the number of degree n polynomials in GF_2[x] that have exactly k linear factors in their prime factorization when the factors are counted with multiplicity, n >= 0, 0 <= k <= n. Triangular array read by rows. | [
"1",
"0",
"2",
"1",
"0",
"3",
"2",
"2",
"0",
"4",
"4",
"4",
"3",
"0",
"5",
"8",
"8",
"6",
"4",
"0",
"6",
"16",
"16",
"12",
"8",
"5",
"0",
"7",
"32",
"32",
"24",
"16",
"10",
"6",
"0",
"8",
"64",
"64",
"48",
"32",
"20",
"12",
"7",
"0",
"9",
"128",
"128",
"96",
"64",
"40",
"24",
"14",
"8",
"0",
"10",
"256",
"256",
"192",
"128",
"80",
"48",
"28",
"16",
"9",
"0",
"11"
]
| [
"nonn",
"tabl"
]
| 13 | 0 | 3 | [
"A001037",
"A356582"
]
| null | Geoffrey Critzer, Aug 13 2022 | 2022-08-23T10:20:22 | oeisdata/seq/A356/A356582.seq | 6691245b0c7f85c28686e5dc62956fb4 |
A356583 | T(n,k) is the number of degree n polynomials p in GF_2[x] whose squarefree part has degree k, n >= 0, 0 <= k <= n. Triangular array read by rows. | [
"1",
"0",
"2",
"2",
"0",
"2",
"2",
"2",
"0",
"4",
"4",
"2",
"2",
"0",
"8",
"4",
"4",
"2",
"6",
"0",
"16",
"10",
"2",
"4",
"6",
"10",
"0",
"32",
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"10",
"4",
"10",
"10",
"22",
"0",
"64",
"20",
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"10",
"10",
"20",
"22",
"42",
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"20",
"18",
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"24",
"16",
"44",
"42",
"86",
"0",
"256",
"40",
"14",
"18",
"18",
"48",
"38",
"80",
"86",
"170",
"0",
"512",
"40",
"36",
"16",
"48",
"32",
"106",
"68",
"166",
"170",
"342",
"0",
"1024"
]
| [
"nonn",
"tabl"
]
| 17 | 0 | 3 | [
"A001037",
"A356583"
]
| null | Geoffrey Critzer, Aug 13 2022 | 2022-08-23T10:20:53 | oeisdata/seq/A356/A356583.seq | 966717182b4ecfc7b53939def77ac1d5 |
A356584 | Number of instances of the stable roommates problem of cardinality n (extension to instances of odd cardinality). | [
"1",
"1",
"2",
"60",
"66360",
"4147236820",
"19902009929142960",
"10325801406739620796634430",
"776107138571279347069904891019268480",
"10911068841557131648034491574230872615312437194176"
]
| [
"nonn"
]
| 85 | 1 | 3 | [
"A200472",
"A356584"
]
| null | Zacharie Moughanim, Aug 13 2022 | 2025-03-23T18:38:42 | oeisdata/seq/A356/A356584.seq | a9ce8dd6ba1abdc32a6f417bcefabdd7 |
A356585 | Number of decimal digits in the n-th Gosper hyperfactorial of n (A330716). | [
"1",
"1",
"2",
"16",
"198",
"2927",
"50060",
"979361",
"21645853",
"534381060",
"14590180163",
"436814197446",
"14235563000269",
"501817445873045",
"19029286646922723",
"772532087068933899",
"33434018751249535666",
"1536767964161539414904",
"74769012084248550773909"
]
| [
"nonn",
"base"
]
| 30 | 0 | 3 | [
"A055642",
"A330716",
"A356585",
"A356586"
]
| null | Greg Huber, Aug 13 2022 | 2022-11-19T21:18:01 | oeisdata/seq/A356/A356585.seq | f8008ffa0fd5bbcec66494ad87f8eba9 |
A356586 | Number of binary digits in the n-th Gosper hyperfactorial of n (A330716). | [
"1",
"1",
"5",
"51",
"657",
"9722",
"166296",
"3253365",
"71905965",
"1775175455",
"48467529392",
"1451065354742",
"47289516677131",
"1667001471950287",
"63213921938077523",
"2566296044236261518",
"111065406214766719510",
"5105032675471072965466",
"248377281869637961805657"
]
| [
"nonn",
"base"
]
| 29 | 0 | 3 | [
"A070939",
"A330716",
"A356585",
"A356586"
]
| null | Greg Huber, Aug 13 2022 | 2022-11-19T21:18:28 | oeisdata/seq/A356/A356586.seq | 2f00f028d77151a447d32c7eafd38fc4 |
A356587 | Expansion of e.g.f. ( Product_{k>0} 1/(1 - (k * x)^k)^(1/k) )^x. | [
"1",
"0",
"2",
"15",
"236",
"8490",
"459234",
"40325880",
"4777773104",
"767688946920",
"156746202491880",
"40056474754165320",
"12448131138826294152",
"4634982982962988690320",
"2033625840922821008112144",
"1039060311676326627685615800",
"611331728108400284878223051520"
]
| [
"nonn"
]
| 10 | 0 | 3 | [
"A023887",
"A354623",
"A355064",
"A356440",
"A356554",
"A356587",
"A356588"
]
| null | Seiichi Manyama, Aug 14 2022 | 2022-08-14T10:15:54 | oeisdata/seq/A356/A356587.seq | 9e043b646b47c7d52f0fb5cc5a4f6191 |
A356588 | Expansion of e.g.f. ( Product_{k>0} 1/(1 - k * x^k)^(1/k) )^x. | [
"1",
"0",
"2",
"9",
"44",
"450",
"2754",
"45360",
"340304",
"6481944",
"81801000",
"1370631240",
"21731534472",
"511117017840",
"8113055559504",
"193958323289640",
"4765385232157440",
"108183734293844160",
"2754467397591689664",
"80416694712647352960",
"2132862160676063137920",
"67803682111729108433280"
]
| [
"nonn"
]
| 10 | 0 | 3 | [
"A055225",
"A355064",
"A356439",
"A356587",
"A356588"
]
| null | Seiichi Manyama, Aug 14 2022 | 2022-08-14T10:15:50 | oeisdata/seq/A356/A356588.seq | f6a9856d9ac5cb33983c6315c9a91626 |
A356589 | a(n) = n! * Sum_{k=1..n} sigma_k(k)/(k * (n-k)!). | [
"1",
"7",
"74",
"1896",
"83829",
"6169915",
"634444586",
"89796130088",
"16407420884385",
"3792452363345383",
"1076168167972120354",
"368657061467873013440",
"149787334364400115372677",
"71262783791831946810277899",
"39228224120114488162020163762"
]
| [
"nonn"
]
| 15 | 1 | 2 | [
"A002745",
"A002746",
"A356437",
"A356589",
"A356590"
]
| null | Seiichi Manyama, Aug 14 2022 | 2022-08-17T02:42:32 | oeisdata/seq/A356/A356589.seq | b690558b22edc030da62bf2c8ed424cf |
A356590 | Expansion of e.g.f. ( Product_{k>0} 1/(1 - (k * x)^k)^(1/k) )^exp(x). | [
"1",
"1",
"8",
"96",
"2382",
"100035",
"6995185",
"699004551",
"96910745876",
"17476222963065",
"4000562831147323",
"1127335505294104887",
"384099492016873956422",
"155403154609857016567601",
"73680868272553092728379865",
"40444727351284600806487687057"
]
| [
"nonn"
]
| 13 | 0 | 3 | [
"A023881",
"A346545",
"A346547",
"A356588",
"A356589",
"A356590"
]
| null | Seiichi Manyama, Aug 14 2022 | 2022-08-14T15:29:24 | oeisdata/seq/A356/A356590.seq | 380c81be9efe4a8489223057bb6cee40 |
A356591 | Numbers k such that A225205(k) is in A354513. | [
"3",
"5",
"7",
"15",
"19",
"20",
"25",
"27",
"34",
"37",
"40",
"44",
"47",
"48",
"52",
"57",
"65",
"77",
"89",
"91",
"92",
"100",
"105",
"107",
"111",
"121",
"123",
"126",
"127",
"129",
"138",
"141",
"153",
"163",
"165",
"167",
"171",
"173",
"179",
"182",
"183",
"185",
"189",
"193",
"195",
"202",
"205",
"209",
"211",
"213",
"215",
"222",
"224",
"226",
"230",
"232",
"234",
"236",
"238"
]
| [
"nonn"
]
| 45 | 1 | 1 | [
"A001622",
"A225204",
"A225205",
"A354513",
"A356591",
"A356664"
]
| null | Jianing Song, Aug 21 2022 | 2022-08-28T08:28:51 | oeisdata/seq/A356/A356591.seq | cdcb9eb7dcaf3fd3afc168773b4a016f |
A356592 | Array A(n, k), n, k >= 0, read by antidiagonals; A(n, k) = Sum_{i, j >= 3} t_i * u_j * T(i+j) where Sum_{i >= 3} t_i * T(i) and Sum_{j >= 3} u_j * T(j) are the greedy tribonacci representations of n and k, respectively, and T = A000073. | [
"0",
"0",
"0",
"0",
"7",
"0",
"0",
"13",
"13",
"0",
"0",
"20",
"24",
"20",
"0",
"0",
"24",
"37",
"37",
"24",
"0",
"0",
"31",
"44",
"57",
"44",
"31",
"0",
"0",
"37",
"57",
"68",
"68",
"57",
"37",
"0",
"0",
"44",
"68",
"88",
"81",
"88",
"68",
"44",
"0",
"0",
"51",
"81",
"105",
"105",
"105",
"105",
"81",
"51",
"0",
"0",
"57",
"94",
"125",
"125",
"136",
"125",
"125",
"94",
"57",
"0"
]
| [
"nonn",
"tabl"
]
| 21 | 0 | 5 | [
"A000045",
"A000073",
"A101330",
"A135090",
"A356592"
]
| null | Rémy Sigrist, Sep 11 2022 | 2022-09-14T08:26:16 | oeisdata/seq/A356/A356592.seq | 8090344d82d08d8b55aa2a6b9e519c37 |
A356593 | Smallest k such that primorial(k) > n^2. | [
"1",
"2",
"3",
"3",
"3",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6"
]
| [
"nonn"
]
| 11 | 1 | 2 | [
"A000290",
"A002110",
"A337769",
"A356593"
]
| null | Christoph B. Kassir, Aug 14 2022 | 2022-08-19T10:09:02 | oeisdata/seq/A356/A356593.seq | 3f68df4bae4e37c491034e4988e54272 |
A356594 | Numbers k for which there exists at least one pair of positive integers (x,y) such that k = x + y and k' = x' + y', and every such pair is coprime. | [
"3",
"25",
"55",
"82",
"85",
"95",
"116",
"121",
"145",
"194",
"226",
"245",
"253",
"289",
"295",
"301",
"305",
"332",
"335",
"343",
"362",
"391",
"407",
"418",
"422",
"446",
"455",
"493",
"529",
"535",
"548",
"583",
"611",
"671",
"731",
"745",
"749",
"754",
"778",
"779",
"781",
"785",
"799",
"805",
"815",
"817",
"818",
"833",
"838",
"845",
"866",
"869",
"899",
"917",
"931",
"943",
"955",
"959",
"985",
"995",
"998"
]
| [
"nonn"
]
| 52 | 1 | 1 | [
"A003415",
"A212662",
"A356594"
]
| null | Giosuè Cavallo, Aug 14 2022 | 2025-03-23T18:24:02 | oeisdata/seq/A356/A356594.seq | f5edd1b36db019d2ae6506345c57c18f |
A356595 | Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k)^k )^exp(x). | [
"1",
"1",
"8",
"60",
"582",
"6555",
"88585",
"1333731",
"22602020",
"420261225",
"8536210843",
"187294058787",
"4420961159582",
"111409233290537",
"2986570482052729",
"84773698697674837",
"2539347801355477960",
"80003306259203052465",
"2644032803825175398175",
"91425359712959262036223"
]
| [
"nonn"
]
| 11 | 0 | 3 | [
"A346545",
"A346547",
"A356337",
"A356595",
"A356600"
]
| null | Seiichi Manyama, Aug 15 2022 | 2022-08-15T08:45:52 | oeisdata/seq/A356/A356595.seq | 3f75d3ac9d199f7386f4e7397e06ce19 |
A356596 | Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k)^(1/k!) )^exp(x). | [
"1",
"1",
"5",
"25",
"162",
"1231",
"10988",
"109481",
"1220005",
"14915924",
"198841997",
"2861122716",
"44290863499",
"731732469209",
"12865489418525",
"239613961313353",
"4712991199268122",
"97557259778360215",
"2120682504988009054",
"48270952330701285107",
"1148400573894718809487"
]
| [
"nonn"
]
| 12 | 0 | 3 | [
"A354338",
"A356025",
"A356596"
]
| null | Seiichi Manyama, Aug 15 2022 | 2022-08-15T10:30:55 | oeisdata/seq/A356/A356596.seq | 8bc743d98f70fb93435f70c7338c2dd2 |
A356597 | Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k/k) )^exp(x). | [
"1",
"1",
"5",
"26",
"172",
"1354",
"12403",
"127945",
"1471006",
"18589503",
"255951308",
"3808299648",
"60871219649",
"1039240205691",
"18868377309780",
"362838034712928",
"7364831540699076",
"157305165900364641",
"3526069495916583260",
"82744901973286823822",
"2028396974232995349291"
]
| [
"nonn"
]
| 10 | 0 | 3 | [
"A354339",
"A356408",
"A356597"
]
| null | Seiichi Manyama, Aug 15 2022 | 2022-08-15T10:30:59 | oeisdata/seq/A356/A356597.seq | fdb93ff77365a69a07d12f2e3e6ef4ab |
A356598 | Expansion of e.g.f. ( Product_{k>0} 1/(1 - k * x^k) )^exp(x). | [
"1",
"1",
"8",
"60",
"606",
"6795",
"96145",
"1458051",
"25584020",
"487911129",
"10231475323",
"230541036627",
"5647620829862",
"146760059424017",
"4075332758190265",
"119876230004510557",
"3727336891407329320",
"121841674696261466385",
"4187995620589733257695",
"150589951713517027739551"
]
| [
"nonn"
]
| 11 | 0 | 3 | [
"A353993",
"A354340",
"A356598"
]
| null | Seiichi Manyama, Aug 15 2022 | 2022-08-15T10:31:03 | oeisdata/seq/A356/A356598.seq | 4664a998501a3d1f1d63e83f4ebb4e10 |
A356599 | Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k/k!) )^exp(x). | [
"1",
"1",
"5",
"25",
"159",
"1201",
"10488",
"102901",
"1121375",
"13406353",
"174284898",
"2445111373",
"36799134584",
"591042564425",
"10086822013726",
"182218681622851",
"3472980343846199",
"69632877583186121",
"1464890891351327598",
"32260213678562913097",
"742152913359395190170"
]
| [
"nonn"
]
| 11 | 0 | 3 | [
"A354341",
"A356409",
"A356599"
]
| null | Seiichi Manyama, Aug 15 2022 | 2022-08-15T10:30:52 | oeisdata/seq/A356/A356599.seq | c0897cbfc25772a16859ac27879f793f |
A356600 | a(n) = n! * Sum_{k=1..n} sigma_2(k)/(k * (n-k)!). | [
"1",
"7",
"38",
"240",
"1509",
"12115",
"96326",
"929432",
"9421089",
"108909943",
"1249105054",
"17862483320",
"241674418101",
"3676733397363",
"59149265744302",
"1058605924855568",
"18041587282787489",
"363409114370324295",
"6970858463185187062",
"153017341796727034336",
"3360005220780469981157"
]
| [
"nonn"
]
| 15 | 1 | 2 | [
"A002745",
"A002746",
"A356298",
"A356589",
"A356600"
]
| null | Seiichi Manyama, Aug 15 2022 | 2022-08-17T03:08:12 | oeisdata/seq/A356/A356600.seq | 9891d5c5424798603487dc21c5621f6f |
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