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666,262,453B
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635M
⌀ | cross_references
listlengths 1
128
⌀ | former_ids
listlengths 1
3
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231
⌀ | timestamp
timestamp[us]date 1999-12-11 03:00:00
2025-07-19 00:40:46
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|---|---|---|---|---|---|---|---|---|---|---|---|---|
A356401 | a(n) = n! * Sum_{k=1..n} Sum_{d|k} (-1)^(d+1)/(d * (k/d)!). | [
"1",
"2",
"9",
"25",
"150",
"841",
"6608",
"41945",
"437986",
"4364741",
"51640952",
"526219585",
"7319856206",
"102469338245",
"1671439939276",
"23909485105217",
"427384036676690",
"7518024186420421",
"149244833247716000",
"2756811766466473601",
"61545779138627817622",
"1354007126970517958885"
]
| [
"nonn"
]
| 9 | 1 | 2 | [
"A356009",
"A356401",
"A356402"
]
| null | Seiichi Manyama, Aug 05 2022 | 2022-08-05T10:48:17 | oeisdata/seq/A356/A356401.seq | 07004030ebd95b3b111a34187528d77c |
A356402 | Expansion of e.g.f. ( Product_{k>0} (1+x^k)^(1/k!) )^(1/(1-x)). | [
"1",
"1",
"3",
"16",
"86",
"626",
"5267",
"50793",
"543279",
"6544805",
"86503762",
"1242678141",
"19259416827",
"321457169151",
"5736414618209",
"108931865485750",
"2191495621647324",
"46604972526167314",
"1043844453093239627",
"24555321244430950299",
"605239630722584461955",
"15600222966916650541099"
]
| [
"nonn"
]
| 10 | 0 | 3 | [
"A298906",
"A356025",
"A356392",
"A356401",
"A356402"
]
| null | Seiichi Manyama, Aug 05 2022 | 2022-08-05T10:48:20 | oeisdata/seq/A356/A356402.seq | e49a3b0421cdfb194bfd525026e6818f |
A356403 | a(n) is the first prime p such that the average of p and the next n-1 primes congruent to p (mod n) is a prime. | [
"5",
"17",
"11",
"19",
"11",
"7",
"5",
"3",
"3",
"13",
"3",
"23",
"7",
"3",
"29",
"5",
"3",
"127",
"17",
"7",
"7",
"7",
"31",
"79",
"5",
"17",
"3",
"17",
"37",
"7",
"23",
"5",
"3",
"5",
"17",
"17",
"11",
"3",
"5",
"107",
"23",
"23",
"7",
"7",
"11",
"11",
"5",
"37",
"11",
"7",
"3",
"19",
"37",
"47",
"37",
"101",
"11",
"71",
"5",
"151",
"13",
"23",
"3",
"23",
"3",
"71",
"11",
"11",
"29",
"13",
"3",
"7",
"97",
"5",
"47",
"17",
"3",
"19",
"11",
"83",
"17",
"11"
]
| [
"nonn"
]
| 8 | 3 | 1 | [
"A356383",
"A356403"
]
| null | J. M. Bergot and Robert Israel, Aug 05 2022 | 2022-08-26T11:22:39 | oeisdata/seq/A356/A356403.seq | b88dadc1dc07d398a2beeaffc7d3d2cf |
A356404 | The number of closed routes of the chess knight, different in shape, consisting of 2 * n jumps on a checkered field without repeating cells of the route. | [
"1",
"3",
"25",
"480",
"11997",
"350275",
"10780478"
]
| [
"nonn",
"walk",
"hard",
"more"
]
| 15 | 1 | 2 | [
"A323131",
"A323559",
"A356404"
]
| null | Nicolay Avilov, Aug 05 2022 | 2024-07-14T08:53:37 | oeisdata/seq/A356/A356404.seq | c8d98f303bcca66ad3cd71512fed88e3 |
A356405 | Primes that are the sum of a set of numbers taken from 1 and 2^(2^k) for k >= 0. | [
"2",
"3",
"5",
"7",
"17",
"19",
"23",
"257",
"263",
"277",
"65537",
"65539",
"65543",
"65557",
"65809",
"4294967569",
"4295032837",
"4295033107",
"340282366920938463463374607431768211729",
"340282366920938463463374607431768277267",
"340282366920938463463374607436063179013",
"340282366920938463481821351505477763347"
]
| [
"nonn",
"base"
]
| 9 | 1 | 1 | [
"A131577",
"A356405"
]
| null | J. M. Bergot and Robert Israel, Aug 05 2022 | 2022-08-26T11:22:48 | oeisdata/seq/A356/A356405.seq | 2c603ae8df2330dc88aeb5c34f416348 |
A356406 | a(n) = n! * Sum_{k=1..n} Sum_{d|k} 1/(d * (k/d)^d). | [
"1",
"4",
"16",
"79",
"443",
"2968",
"22216",
"189698",
"1792402",
"18745036",
"213452996",
"2653142952",
"35448861576",
"509724975264",
"7824794618208",
"128006170541328",
"2217950478978576",
"40686737647774368",
"785852762719168992",
"15974195890305405696",
"340376906088298319616"
]
| [
"nonn"
]
| 14 | 1 | 2 | [
"A308345",
"A356009",
"A356010",
"A356406",
"A356407",
"A356408"
]
| null | Seiichi Manyama, Aug 05 2022 | 2022-08-05T15:36:54 | oeisdata/seq/A356/A356406.seq | e7136d3b9a26f2a3d72118d50e270fe6 |
A356407 | a(n) = n! * Sum_{k=1..n} Sum_{d|k} 1/(d * ((k/d)!)^d). | [
"1",
"4",
"15",
"70",
"375",
"2411",
"17598",
"146490",
"1359291",
"13978597",
"157393368",
"1929989029",
"25568858978",
"364288345409",
"5551537358188",
"90142504077194",
"1553345359200299",
"28317316174307405",
"544431381017568696",
"11010510372888267555",
"233653645911730002976"
]
| [
"nonn"
]
| 15 | 1 | 2 | [
"A182926",
"A356009",
"A356406",
"A356407",
"A356409"
]
| null | Seiichi Manyama, Aug 05 2022 | 2022-08-05T15:36:57 | oeisdata/seq/A356/A356407.seq | 15b3ce5a5f1d58539f9d0f23ac99c82f |
A356408 | Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k/k) )^(1/(1-x)). | [
"1",
"1",
"5",
"29",
"216",
"1919",
"20012",
"236977",
"3145832",
"46122546",
"739703182",
"12865212172",
"241040899668",
"4836265824740",
"103410589256452",
"2346358252787094",
"56285005757022752",
"1422783492250963296",
"37790069818311971640",
"1051924374853915254048"
]
| [
"nonn"
]
| 12 | 0 | 3 | [
"A007841",
"A356336",
"A356406",
"A356408",
"A356409"
]
| null | Seiichi Manyama, Aug 05 2022 | 2022-08-05T15:37:04 | oeisdata/seq/A356/A356408.seq | 9d74770899f1d03dc7b382d179e645f8 |
A356409 | Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k/k!) )^(1/(1-x)). | [
"1",
"1",
"5",
"28",
"203",
"1756",
"17802",
"205010",
"2644287",
"37669096",
"586855058",
"9914829508",
"180429770402",
"3516313661706",
"73029591042943",
"1609531482261375",
"37504691293842367",
"920966310015565936",
"23764054962685200642",
"642681497080268685092",
"18174504398294667649782"
]
| [
"nonn"
]
| 12 | 0 | 3 | [
"A005651",
"A356025",
"A356407",
"A356408",
"A356409"
]
| null | Seiichi Manyama, Aug 05 2022 | 2022-08-05T15:37:08 | oeisdata/seq/A356/A356409.seq | ea07c8499aa009590a2fe5396de651a1 |
A356410 | Numbers k for which k^3 is divisible by sigma(k). | [
"1",
"6",
"28",
"30",
"84",
"102",
"120",
"364",
"420",
"496",
"672",
"840",
"1080",
"1092",
"1320",
"1428",
"1488",
"1782",
"2280",
"2716",
"2760",
"3276",
"3360",
"3444",
"3472",
"3480",
"3720",
"4452",
"5640",
"7080",
"7392",
"7440",
"7560",
"8128",
"8148",
"8736",
"8910",
"9240",
"9480",
"10416",
"10920",
"11880",
"12400",
"15456",
"15960"
]
| [
"nonn"
]
| 26 | 1 | 2 | [
"A000203",
"A000578",
"A090777",
"A356410"
]
| null | Zdenek Cervenka, Aug 05 2022 | 2024-09-04T16:20:55 | oeisdata/seq/A356/A356410.seq | 9bbc8894e904594ff0167884442bdd0c |
A356411 | Sum of powers of roots of x^3 - x^2 - x - 3. | [
"3",
"1",
"3",
"13",
"19",
"41",
"99",
"197",
"419",
"913",
"1923",
"4093",
"8755",
"18617",
"39651",
"84533",
"180035",
"383521",
"817155",
"1740781",
"3708499",
"7900745",
"16831587",
"35857829",
"76391651",
"162744241",
"346709379",
"738628573",
"1573570675",
"3352327385",
"7141783779"
]
| [
"nonn",
"easy"
]
| 24 | 0 | 1 | [
"A103143",
"A123102",
"A247594",
"A273065",
"A356411",
"A356463"
]
| null | Greg Dresden, Aug 05 2022 | 2022-08-11T07:25:45 | oeisdata/seq/A356/A356411.seq | 0b9d86e36abcad349c1ae84a70e5d702 |
A356412 | First differences of A007770 (happy numbers). | [
"6",
"3",
"3",
"6",
"4",
"5",
"3",
"1",
"12",
"5",
"19",
"2",
"9",
"3",
"4",
"5",
"3",
"3",
"3",
"3",
"6",
"20",
"1",
"3",
"6",
"28",
"9",
"12",
"2",
"2",
"1",
"10",
"5",
"11",
"7",
"4",
"6",
"3",
"23",
"1",
"17",
"11",
"2",
"8",
"1",
"8",
"3",
"6",
"1",
"6",
"3",
"2",
"7",
"18",
"6",
"3",
"2",
"1",
"8",
"3",
"4",
"3",
"5",
"1",
"5",
"7",
"5",
"31",
"6",
"18",
"5",
"9",
"9",
"3",
"6",
"40",
"20",
"7",
"2",
"1",
"42",
"9",
"5",
"1",
"9",
"3",
"2",
"1"
]
| [
"nonn",
"base"
]
| 15 | 1 | 1 | [
"A007770",
"A356412"
]
| null | Darío D. Devia, Aug 05 2022 | 2022-08-30T14:29:05 | oeisdata/seq/A356/A356412.seq | c2754117641308239a2a0dac3a1fb30a |
A356413 | Numbers with an equal sum of the even and odd exponents in their prime factorizations. | [
"1",
"60",
"84",
"90",
"126",
"132",
"140",
"150",
"156",
"198",
"204",
"220",
"228",
"234",
"260",
"276",
"294",
"306",
"308",
"315",
"340",
"342",
"348",
"350",
"364",
"372",
"380",
"414",
"444",
"460",
"476",
"490",
"492",
"495",
"516",
"522",
"525",
"532",
"550",
"558",
"564",
"572",
"580",
"585",
"620",
"636",
"644",
"650",
"666",
"693",
"708",
"726",
"732",
"735"
]
| [
"nonn"
]
| 10 | 1 | 2 | [
"A028260",
"A048109",
"A085987",
"A179698",
"A187039",
"A190109",
"A190110",
"A348097",
"A350386",
"A350387",
"A356413"
]
| null | Amiram Eldar, Aug 06 2022 | 2022-08-07T07:53:13 | oeisdata/seq/A356/A356413.seq | b7c2c8e3ee78516a39f401de234a5e31 |
A356414 | Number k such that k and k+1 both have an equal sum of even and odd exponents in their prime factorization (A356413). | [
"819",
"1035",
"1196",
"1274",
"1275",
"1449",
"1665",
"1924",
"1925",
"1988",
"2324",
"2331",
"2540",
"3068",
"3195",
"3324",
"3339",
"3549",
"3555",
"3626",
"3717",
"4164",
"4220",
"4235",
"4556",
"4598",
"4635",
"4675",
"4796",
"5084",
"5525",
"5634",
"5660",
"6003",
"6027",
"6068",
"6164",
"6363",
"6740",
"6867",
"6908",
"7028",
"7227",
"7275"
]
| [
"nonn"
]
| 8 | 1 | 1 | [
"A350386",
"A350387",
"A356413",
"A356414"
]
| null | Amiram Eldar, Aug 06 2022 | 2022-08-07T07:53:19 | oeisdata/seq/A356/A356414.seq | 950606cf5bc8f548f036efab0dd3becd |
A356415 | a(n) is the least start of exactly n consecutive numbers that have an equal number of even and odd exponents in their prime factorization (A187039), or -1 if no such run of consecutive numbers exists. | [
"1",
"44",
"603",
"906596",
"792007675"
]
| [
"nonn",
"more"
]
| 4 | 1 | 2 | [
"A187039",
"A348076",
"A348077",
"A348078",
"A356415"
]
| null | Amiram Eldar, Aug 06 2022 | 2022-08-06T08:09:34 | oeisdata/seq/A356/A356415.seq | fde83b284d92c351b095824d98a4141b |
A356416 | a(n) is the least start of exactly n consecutive numbers that have an equal sum of even and odd exponents in their prime factorization (A356413), or -1 if no such run of consecutive numbers exists. | [
"1",
"819",
"1274",
"19940",
"204323",
"149228720",
"3144583275"
]
| [
"nonn",
"more"
]
| 10 | 1 | 2 | [
"A356413",
"A356415",
"A356416"
]
| null | Amiram Eldar, Aug 06 2022 | 2023-08-28T08:21:08 | oeisdata/seq/A356/A356416.seq | 9ce9bc0dc0d08ee2590e3eb10a69353f |
A356417 | Numbers whose reversal is a square. | [
"0",
"1",
"4",
"9",
"10",
"18",
"40",
"46",
"52",
"61",
"63",
"90",
"94",
"100",
"121",
"144",
"148",
"163",
"169",
"180",
"400",
"423",
"441",
"460",
"484",
"487",
"520",
"522",
"526",
"610",
"630",
"652",
"675",
"676",
"691",
"900",
"925",
"927",
"940",
"961",
"982",
"1000",
"1042",
"1062",
"1089",
"1210",
"1251",
"1273",
"1297",
"1405",
"1426",
"1440",
"1480"
]
| [
"nonn",
"base"
]
| 43 | 1 | 3 | [
"A002942",
"A004086",
"A074896",
"A356417"
]
| null | Daniel Blam, Aug 06 2022 | 2022-08-07T12:59:43 | oeisdata/seq/A356/A356417.seq | 3e9ce1c50a6fcce3b56b2b7e64c4b14d |
A356418 | Decimal expansion of sqrt(4/3 + 1/sqrt(3)). | [
"1",
"3",
"8",
"2",
"2",
"7",
"4",
"7",
"9",
"2",
"6",
"9",
"6",
"0",
"6",
"8",
"4",
"8",
"2",
"3",
"6",
"5",
"1",
"0",
"8",
"0",
"4",
"4",
"9",
"1",
"8",
"0",
"4",
"1",
"9",
"0",
"3",
"9",
"5",
"1",
"4",
"1",
"5",
"1",
"5",
"2",
"1",
"7",
"1",
"8",
"1",
"3",
"1",
"0",
"3",
"3",
"3",
"0",
"3",
"2",
"3",
"4",
"4",
"9",
"8",
"5",
"3",
"5",
"4",
"0",
"6",
"9",
"7",
"8",
"7",
"8",
"5",
"6",
"6",
"6",
"6",
"8",
"3",
"2",
"7",
"0",
"0",
"8",
"4",
"5",
"0",
"0",
"5",
"3",
"6",
"0",
"1"
]
| [
"nonn",
"cons",
"easy"
]
| 60 | 1 | 2 | [
"A002194",
"A020760",
"A356418"
]
| null | Christoph B. Kassir, Aug 21 2022 | 2022-08-26T10:27:20 | oeisdata/seq/A356/A356418.seq | f6097477566a385ba64862f24efb9601 |
A356419 | Inverse of A067576 considered as a permutation of the positive integers. | [
"1",
"2",
"3",
"4",
"5",
"8",
"6",
"7",
"12",
"17",
"9",
"23",
"13",
"18",
"10",
"11",
"30",
"38",
"24",
"47",
"31",
"39",
"14",
"57",
"48",
"58",
"19",
"69",
"25",
"32",
"15",
"16",
"68",
"80",
"81",
"93",
"94",
"108",
"40",
"107",
"123",
"139",
"49",
"156",
"59",
"70",
"20",
"122",
"174",
"193",
"82",
"213",
"95",
"109",
"26",
"234",
"124",
"140",
"33",
"157",
"41",
"50",
"21",
"22",
"138",
"155",
"256"
]
| [
"nonn",
"look",
"easy"
]
| 20 | 1 | 2 | [
"A000120",
"A067576",
"A067587",
"A068076",
"A263017",
"A356419"
]
| null | Jianing Song, Aug 06 2022 | 2023-03-02T11:55:08 | oeisdata/seq/A356/A356419.seq | 1eeea2852f8b45f5521eeadad2413470 |
A356420 | Integers k such that for some m >= 0, psi(k) = rad(k)^m, where psi(k) = A001615(k) and rad(k) = A007947(k). | [
"1",
"18",
"108",
"648",
"3888",
"11250",
"23328",
"139968",
"337500",
"501126",
"839808",
"5038848",
"8696754",
"10125000",
"30233088",
"51114852",
"57177414",
"181398528",
"303750000",
"573985764",
"1088391168",
"2401451388",
"5018345916",
"5213714904",
"6530347008",
"9112500000",
"23981814018",
"26622318750",
"37883060424"
]
| [
"nonn"
]
| 17 | 1 | 2 | [
"A001615",
"A007947",
"A355045",
"A356420"
]
| null | Michel Marcus, Aug 06 2022 | 2022-08-13T15:48:06 | oeisdata/seq/A356/A356420.seq | b1a919592932657cba155ad62519df30 |
A356421 | Positive integers k such that k + p is a power of 2, where p is the least prime greater than k. | [
"3",
"15",
"61",
"255",
"2043",
"4093",
"32765",
"65535",
"262141",
"8388599",
"33554397",
"134217699",
"268435453",
"1073741821",
"17179869159",
"137438953463",
"274877906937",
"1099511627761",
"8796093022179",
"17592186044409",
"70368744177649",
"140737488355323",
"281474976710635",
"562949953421243"
]
| [
"nonn"
]
| 28 | 1 | 1 | [
"A000040",
"A000079",
"A014210",
"A356421",
"A356434"
]
| null | Ali Sada, Aug 06 2022 | 2022-09-11T10:31:08 | oeisdata/seq/A356/A356421.seq | cddff8a308a70a449aa4d17e42083372 |
A356422 | Heptagonal numbers which are products of three distinct primes. | [
"286",
"874",
"970",
"1918",
"3367",
"3553",
"4558",
"6682",
"8323",
"8614",
"11122",
"11458",
"12145",
"14707",
"16687",
"17098",
"17935",
"18361",
"19669",
"21022",
"27931",
"30085",
"33466",
"38254",
"42055",
"42706",
"44023",
"44689",
"46717",
"48094",
"50197",
"55279",
"61387",
"64561",
"73702",
"79834",
"81631",
"82537",
"85285",
"88078",
"89965",
"92833",
"101707",
"105781",
"108889"
]
| [
"nonn"
]
| 19 | 1 | 1 | [
"A000566",
"A007304",
"A356422"
]
| null | Massimo Kofler, Aug 07 2022 | 2025-03-10T12:26:57 | oeisdata/seq/A356/A356422.seq | f8cd2e2fee002d8e4e929013f4f753f2 |
A356423 | Leyland numbers which are products of two distinct primes. | [
"57",
"145",
"177",
"1649",
"7073",
"23401",
"131361",
"423393",
"2012174",
"4785713",
"33555057",
"43050817",
"177264449",
"364568617",
"1073792449",
"4486784401",
"13877119009",
"31381070257",
"94143190994",
"125937424601",
"2552470327702",
"8796093024057",
"33233199005057",
"130291290501553",
"1628414210130481",
"1853020188884609"
]
| [
"nonn"
]
| 6 | 1 | 1 | [
"A006881",
"A076980",
"A356423"
]
| null | Massimo Kofler, Aug 07 2022 | 2022-10-02T00:53:55 | oeisdata/seq/A356/A356423.seq | a77d3f61067206d3ac094493e8683172 |
A356424 | 9-gonal numbers that are semiprimes. | [
"9",
"46",
"111",
"559",
"1639",
"3961",
"4699",
"7291",
"11629",
"12871",
"23329",
"30691",
"32689",
"41311",
"48439",
"85879",
"114211",
"129889",
"142309",
"159751",
"262081",
"267859",
"310069",
"342109",
"389611",
"418141",
"486019",
"542341",
"584461",
"619291",
"729829",
"758881",
"923401",
"967051",
"1011709",
"1104049",
"1163809"
]
| [
"nonn"
]
| 17 | 1 | 1 | [
"A001106",
"A001358",
"A356424"
]
| null | Massimo Kofler, Aug 07 2022 | 2023-01-16T04:28:35 | oeisdata/seq/A356/A356424.seq | 0abd6560b5dd0b2dec6f96ca5013bf64 |
A356425 | Sum of divisors of numbers of least prime signature: a(n) = A000203(A025487(n)). | [
"1",
"3",
"7",
"12",
"15",
"28",
"31",
"60",
"72",
"63",
"91",
"124",
"168",
"127",
"195",
"252",
"360",
"255",
"403",
"546",
"508",
"576",
"600",
"744",
"511",
"819",
"1170",
"1020",
"1344",
"1240",
"1512",
"1023",
"1651",
"2418",
"2044",
"2880",
"2520",
"2821",
"3048",
"2047",
"3600",
"3315",
"4368",
"3751",
"4914",
"4092",
"5952",
"5080",
"6045",
"6120"
]
| [
"nonn"
]
| 52 | 1 | 2 | [
"A000005",
"A000203",
"A025487",
"A146288",
"A356425"
]
| null | Hal M. Switkay, Dec 11 2022 | 2022-12-15T17:00:35 | oeisdata/seq/A356/A356425.seq | 9c1a7de301cb1bbe2eee212e66c512dd |
A356426 | Even bisection of A003278. | [
"2",
"5",
"11",
"14",
"29",
"32",
"38",
"41",
"83",
"86",
"92",
"95",
"110",
"113",
"119",
"122",
"245",
"248",
"254",
"257",
"272",
"275",
"281",
"284",
"326",
"329",
"335",
"338",
"353",
"356",
"362",
"365",
"731",
"734",
"740",
"743",
"758",
"761",
"767",
"770",
"812",
"815",
"821",
"824",
"839",
"842",
"848",
"851",
"974",
"977",
"983",
"986",
"1001",
"1004",
"1010",
"1013",
"1055",
"1058"
]
| [
"nonn"
]
| 25 | 1 | 1 | [
"A003278",
"A191107",
"A356426"
]
| null | Arie Bos, Aug 07 2022 | 2022-09-07T12:27:24 | oeisdata/seq/A356/A356426.seq | 26d84f71c7b4c67d02b5cd7b43b66d37 |
A356427 | a(0) = 0, a(1) = 1; for n > 1, a(n) is the last step before reaching 0 of the iterations x -> x - gpf(x) starting at n, where gpf = A006530. | [
"0",
"1",
"2",
"3",
"2",
"5",
"3",
"7",
"3",
"3",
"5",
"11",
"3",
"13",
"7",
"5",
"7",
"17",
"5",
"19",
"5",
"7",
"11",
"23",
"7",
"5",
"13",
"7",
"7",
"29",
"5",
"31",
"5",
"11",
"17",
"7",
"11",
"37",
"19",
"13",
"7",
"41",
"7",
"43",
"11",
"7",
"23",
"47",
"7",
"7",
"7",
"17",
"13",
"53",
"17",
"11",
"7",
"19",
"29",
"59",
"11",
"61",
"31",
"7",
"31",
"13",
"11",
"67",
"17",
"23",
"7",
"71",
"23",
"73",
"37",
"7",
"19",
"11"
]
| [
"nonn"
]
| 11 | 0 | 3 | [
"A006530",
"A076563",
"A309892",
"A356427",
"A356438",
"A356441"
]
| null | Jianing Song, Aug 07 2022 | 2022-08-07T22:11:00 | oeisdata/seq/A356/A356427.seq | 5109483437c27fbe79d481c77fa64261 |
A356428 | a(0) = a(1) = 0; for n > 1, a(n) is the number of distinct gpf(x)'s in the iterations x -> x - gpf(x) starting at n and ending at 0, where gpf = A006530. | [
"0",
"0",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"3",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"2",
"1"
]
| [
"nonn"
]
| 23 | 0 | 9 | [
"A006530",
"A076563",
"A309892",
"A356428",
"A356429"
]
| null | Jianing Song, Aug 07 2022 | 2022-08-09T15:33:36 | oeisdata/seq/A356/A356428.seq | 033c4e8c248023f55e11abcd9f836cfd |
A356429 | Smallest m such that A356428(m) = n, or -1 if there is no such m. | [
"2",
"8",
"48",
"315",
"320",
"6664",
"135450",
"273000",
"518661",
"519440",
"519622",
"148830266",
"558797841",
"558797968",
"24900609294"
]
| [
"nonn",
"hard",
"more",
"changed"
]
| 25 | 1 | 1 | [
"A006530",
"A076563",
"A309892",
"A356428",
"A356429"
]
| null | Jianing Song, Aug 07 2022 | 2025-07-07T10:52:16 | oeisdata/seq/A356/A356429.seq | 7f58a7e48473fd2fc60b0e0ab9f34bc6 |
A356430 | a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not occurring earlier that shares a factor with the number of divisors of a(n-1). | [
"1",
"2",
"4",
"3",
"6",
"8",
"10",
"12",
"9",
"15",
"14",
"16",
"5",
"18",
"20",
"21",
"22",
"24",
"26",
"28",
"27",
"30",
"32",
"33",
"34",
"36",
"39",
"38",
"40",
"42",
"44",
"45",
"46",
"48",
"25",
"51",
"50",
"52",
"54",
"56",
"58",
"60",
"57",
"62",
"64",
"7",
"66",
"68",
"63",
"69",
"70",
"72",
"74",
"76",
"75",
"78",
"80",
"35",
"82",
"84",
"81",
"55",
"86",
"88",
"90",
"87",
"92",
"93",
"94",
"96",
"98",
"99",
"100",
"102",
"104"
]
| [
"nonn"
]
| 7 | 1 | 2 | [
"A000005",
"A348086",
"A354960",
"A356430",
"A356431",
"A356432"
]
| null | Scott R. Shannon, Aug 07 2022 | 2023-01-16T09:10:46 | oeisdata/seq/A356/A356430.seq | 0c75655a543d379d75dbe09a1e096493 |
A356431 | a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not occurring earlier that shares a factor with both a(n-1) and the number of divisors of a(n-1). | [
"1",
"2",
"4",
"6",
"8",
"10",
"12",
"3",
"18",
"9",
"15",
"20",
"14",
"16",
"30",
"22",
"24",
"26",
"28",
"21",
"36",
"27",
"42",
"32",
"34",
"38",
"40",
"44",
"33",
"48",
"45",
"39",
"52",
"46",
"50",
"54",
"56",
"58",
"60",
"51",
"66",
"62",
"64",
"70",
"68",
"72",
"57",
"76",
"74",
"78",
"80",
"5",
"90",
"63",
"69",
"84",
"75",
"81",
"105",
"96",
"82",
"86",
"88",
"92",
"94",
"98",
"100",
"102",
"104",
"106",
"108",
"87",
"114",
"110"
]
| [
"nonn"
]
| 9 | 1 | 2 | [
"A000005",
"A348086",
"A354960",
"A356430",
"A356431",
"A356432"
]
| null | Scott R. Shannon, Aug 07 2022 | 2023-01-16T09:10:46 | oeisdata/seq/A356/A356431.seq | 759f3b5ef7070dce483fe763d8ba8f07 |
A356432 | a(1) = 1; for n > 1, a(n) is the smallest positive number not occurring earlier that shares a factor with a(n-1) plus the number of divisors of a(n-1). | [
"1",
"2",
"4",
"7",
"3",
"5",
"14",
"6",
"8",
"9",
"10",
"12",
"15",
"19",
"18",
"16",
"21",
"20",
"13",
"24",
"22",
"26",
"25",
"28",
"17",
"38",
"27",
"31",
"11",
"39",
"43",
"30",
"32",
"34",
"36",
"33",
"37",
"42",
"35",
"45",
"48",
"29",
"62",
"40",
"44",
"46",
"50",
"49",
"52",
"54",
"56",
"58",
"60",
"51",
"55",
"59",
"61",
"57",
"122",
"63",
"23",
"65",
"66",
"64",
"71",
"73",
"69",
"146",
"68",
"70",
"72",
"74",
"75",
"78",
"76",
"41"
]
| [
"nonn"
]
| 13 | 1 | 2 | [
"A000005",
"A348086",
"A354960",
"A356430",
"A356431",
"A356432"
]
| null | Scott R. Shannon, Aug 07 2022 | 2023-01-16T14:56:50 | oeisdata/seq/A356/A356432.seq | 64d1180a9b333935115db6b33c99aeec |
A356433 | Numbers k such that, in the prime factorization of k, the least common multiple of the exponents equals the least common multiple of the prime factors. | [
"1",
"4",
"27",
"72",
"108",
"192",
"576",
"800",
"1458",
"1728",
"2916",
"3125",
"5120",
"5832",
"6272",
"12500",
"21600",
"25600",
"30375",
"36000",
"46656",
"48600",
"77760",
"84375",
"114688",
"116640",
"121500",
"138240",
"169344",
"225000",
"247808",
"337500",
"384000",
"388800",
"395136",
"583200",
"600000",
"653184",
"691200",
"750141",
"802816",
"823543",
"857304",
"979776"
]
| [
"nonn"
]
| 28 | 1 | 2 | [
"A007947",
"A051674",
"A054411",
"A054412",
"A068935",
"A068936",
"A068937",
"A068938",
"A072411",
"A082949",
"A356433"
]
| null | Jean-Marc Rebert, Aug 07 2022 | 2023-02-02T04:25:33 | oeisdata/seq/A356/A356433.seq | 8f35526826417a6e7d5f9f97ad7f1a96 |
A356434 | Prime nearest to 2^n. In case of a tie, choose the larger. | [
"2",
"2",
"5",
"7",
"17",
"31",
"67",
"127",
"257",
"509",
"1021",
"2053",
"4099",
"8191",
"16381",
"32771",
"65537",
"131071",
"262147",
"524287",
"1048573",
"2097143",
"4194301",
"8388617",
"16777213",
"33554467",
"67108859",
"134217757",
"268435459",
"536870909",
"1073741827",
"2147483647",
"4294967291",
"8589934583"
]
| [
"nonn"
]
| 17 | 0 | 1 | [
"A014210",
"A014234",
"A117387",
"A226178",
"A340707",
"A356434"
]
| null | Peter Munn, Aug 07 2022 | 2023-02-19T15:10:48 | oeisdata/seq/A356/A356434.seq | d95b078483c41eb77ffd50ece791d185 |
A356435 | a(n) is the minimum number of Z x Z lattice points inside or on a circle of radius n^(1/2) for any position of the center of the circle. | [
"0",
"2",
"4",
"8",
"10",
"14",
"16",
"20",
"22",
"26",
"29",
"32",
"32",
"39",
"41",
"44",
"46",
"51",
"52",
"56",
"58",
"62",
"66",
"69",
"69",
"74",
"79",
"82",
"85",
"88",
"88",
"92",
"96",
"100",
"103",
"106",
"108",
"113",
"116",
"119",
"120",
"122",
"124",
"132",
"135",
"138",
"141",
"143",
"145",
"146",
"152",
"158",
"160",
"164",
"164",
"166",
"172",
"175",
"179",
"181",
"184",
"186",
"189",
"193",
"194",
"199"
]
| [
"nonn"
]
| 30 | 0 | 2 | [
"A057655",
"A123689",
"A291259",
"A356435"
]
| null | Bernard Montaron, Aug 07 2022 | 2025-02-17T08:30:02 | oeisdata/seq/A356/A356435.seq | 187f09e1601ba64f15a2820b904de750 |
A356436 | a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} d^(k/d) )/k. | [
"1",
"5",
"23",
"146",
"874",
"8124",
"62628",
"707664",
"7860816",
"103284000",
"1179669600",
"24454569600",
"324615427200",
"5740203974400",
"119579523436800",
"2688723275212800",
"46084905896601600",
"1383333631684300800",
"26411386476116275200",
"868104140064602112000"
]
| [
"nonn"
]
| 15 | 1 | 2 | [
"A055225",
"A353992",
"A356297",
"A356436",
"A356437",
"A356439"
]
| null | Seiichi Manyama, Aug 07 2022 | 2022-08-07T12:30:17 | oeisdata/seq/A356/A356436.seq | 36610be835e2140e5fba1b39a846ddd7 |
A356437 | a(n) = n! * Sum_{k=1..n} sigma_k(k)/k. | [
"1",
"7",
"77",
"1946",
"84754",
"6202524",
"636369348",
"89979720144",
"16431405256656",
"3796658174518560",
"1077102230236529760",
"368915006390671969920",
"149873555740938949215360",
"71297150722148582901815040",
"39244301012876892023553235200"
]
| [
"nonn"
]
| 14 | 1 | 2 | [
"A023887",
"A356297",
"A356436",
"A356437",
"A356440"
]
| null | Seiichi Manyama, Aug 07 2022 | 2022-08-07T12:59:05 | oeisdata/seq/A356/A356437.seq | 46aeac403d48f1b2997587c7616e661a |
A356438 | Numbers k such that A309892(k) = k/gpf(k), where gpf = A006530. | [
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"9",
"10",
"11",
"12",
"13",
"14",
"15",
"17",
"19",
"20",
"21",
"22",
"23",
"25",
"26",
"28",
"29",
"30",
"31",
"33",
"34",
"35",
"37",
"38",
"39",
"41",
"42",
"43",
"44",
"46",
"47",
"49",
"51",
"52",
"53",
"55",
"56",
"57",
"58",
"59",
"61",
"62",
"63",
"65",
"66",
"67",
"68",
"69",
"70",
"71",
"73",
"74",
"76",
"77",
"78",
"79",
"82",
"83",
"85"
]
| [
"nonn",
"easy"
]
| 11 | 1 | 2 | [
"A000040",
"A001358",
"A006530",
"A076563",
"A151800",
"A309892",
"A356428",
"A356438",
"A356441"
]
| null | Jianing Song, Aug 07 2022 | 2022-08-07T22:10:38 | oeisdata/seq/A356/A356438.seq | 7a095e1c65919f8411b572f653e0a57a |
A356439 | Expansion of e.g.f. ( Product_{k>0} 1/(1 - k * x^k)^(1/k) )^(1/(1-x)). | [
"1",
"1",
"6",
"39",
"344",
"3410",
"42234",
"567126",
"8812880",
"149409144",
"2793232440",
"56224856160",
"1234342760232",
"28773852409848",
"718719835537872",
"19045601930731320",
"534564416062012800",
"15792205306586537280",
"491639547448322794944",
"16024048206145815040704"
]
| [
"nonn"
]
| 8 | 0 | 3 | [
"A353993",
"A356436",
"A356439",
"A356440"
]
| null | Seiichi Manyama, Aug 07 2022 | 2022-08-07T12:59:15 | oeisdata/seq/A356/A356439.seq | 50bb27d3983394f8cc6759779d80f795 |
A356440 | Expansion of e.g.f. ( Product_{k>0} 1/(1 - (k * x)^k)^(1/k) )^(1/(1-x)). | [
"1",
"1",
"8",
"99",
"2444",
"101450",
"7045194",
"701736966",
"97147459184",
"17505366041880",
"4005462950166600",
"1128394974054308400",
"384386423684496873672",
"155497732356686080354968",
"73718160600338917089657216",
"40462026280443230503858113240"
]
| [
"nonn"
]
| 8 | 0 | 3 | [
"A356437",
"A356439",
"A356440"
]
| null | Seiichi Manyama, Aug 07 2022 | 2022-08-07T12:59:25 | oeisdata/seq/A356/A356440.seq | 3d2bdf3f36393bb2d4260c71ffb327e1 |
A356441 | Numbers k such that A309892(k) < k/gpf(k), where gpf = A006530; complement of A356438. | [
"8",
"16",
"18",
"24",
"27",
"32",
"36",
"40",
"45",
"48",
"50",
"54",
"60",
"64",
"72",
"75",
"80",
"81",
"84",
"90",
"96",
"98",
"100",
"105",
"108",
"112",
"120",
"125",
"126",
"128",
"135",
"140",
"144",
"147",
"150",
"154",
"160",
"162",
"165",
"168",
"175",
"176",
"180",
"189",
"192",
"196",
"198",
"200",
"210",
"216",
"220",
"224",
"225",
"231",
"234",
"240",
"242",
"243"
]
| [
"nonn",
"easy"
]
| 10 | 1 | 1 | [
"A006530",
"A076563",
"A151800",
"A309892",
"A356438",
"A356441"
]
| null | Jianing Song, Aug 07 2022 | 2022-08-07T20:58:23 | oeisdata/seq/A356/A356441.seq | a1dbd6b4ca2e04238b7903565a8b67f0 |
A356442 | a(n) is the least positive even number that is the unordered sum of two primes congruent mod 10 in exactly n ways. | [
"2",
"4",
"26",
"86",
"126",
"174",
"264",
"324",
"396",
"456",
"546",
"594",
"624",
"876",
"966",
"984",
"924",
"954",
"1326",
"1344",
"1386",
"1512",
"1596",
"1638",
"1848",
"1764",
"2046",
"2226",
"2838",
"2574",
"2706",
"2604",
"2772",
"2436",
"3366",
"3066",
"2964",
"3432",
"3894",
"3738",
"3234",
"3696",
"3654",
"4074",
"4446",
"4158",
"4368",
"4494",
"4788",
"5016",
"4746",
"5754",
"4914"
]
| [
"nonn",
"base"
]
| 12 | 0 | 1 | [
"A023036",
"A356442"
]
| null | J. M. Bergot and Robert Israel, Aug 07 2022 | 2022-08-31T09:07:23 | oeisdata/seq/A356/A356442.seq | 1590610b9068c886dba31fb3f2fb2ab1 |
A356443 | Primes p such that the concatenation of p and 2*p is the average of a twin prime pair. | [
"569",
"661",
"1249",
"1559",
"1571",
"1949",
"1999",
"2389",
"2441",
"2609",
"2879",
"3761",
"3911",
"5689",
"5701",
"5749",
"5779",
"6389",
"6481",
"6971",
"7559",
"7561",
"7741",
"8191",
"8971",
"9221",
"9391",
"9521",
"10061",
"10111",
"10289",
"10601",
"10949",
"11821",
"11941",
"12071",
"12281",
"12689",
"12721",
"12809",
"13151",
"13469",
"13681",
"14821",
"15569",
"16931",
"18661"
]
| [
"nonn",
"base"
]
| 12 | 1 | 1 | [
"A014574",
"A356443"
]
| null | J. M. Bergot and Robert Israel, Aug 07 2022 | 2022-08-31T09:07:27 | oeisdata/seq/A356/A356443.seq | 4c5c7b8347736f12435d97ef02241854 |
A356444 | Number of ways to create an angle excess of n degrees using 3 regular polygons with integral internal angles. | [
"0",
"1",
"3",
"1",
"3",
"6",
"1",
"3",
"4",
"6",
"2",
"9",
"2",
"5",
"7",
"5",
"2",
"9",
"2",
"6",
"6",
"4",
"2",
"8",
"4",
"5",
"7",
"7",
"2",
"12",
"3",
"6",
"7",
"5",
"7",
"10",
"4",
"6",
"9",
"10",
"5",
"12",
"6",
"10",
"11",
"8",
"6",
"14",
"6",
"11",
"9",
"8",
"6",
"12",
"8",
"7",
"8",
"8",
"5",
"15",
"3",
"7",
"8",
"8",
"7",
"12",
"6",
"8",
"10",
"12",
"7",
"14",
"6",
"10",
"13"
]
| [
"nonn"
]
| 24 | 1 | 3 | [
"A356444",
"A356663"
]
| null | Joseph C. Y. Wong, Aug 21 2022 | 2022-10-02T00:42:29 | oeisdata/seq/A356/A356444.seq | 5928a776ad84e4fa03aa34ea039f1670 |
A356445 | a(n) is the number of times that A064440(n) occurs as the sum of proper divisors function (A001065). | [
"2",
"3",
"5",
"7",
"13",
"17",
"19",
"23",
"31",
"41",
"59",
"61",
"67",
"79",
"83",
"97",
"101",
"109",
"113",
"127",
"131",
"139",
"149",
"151",
"193",
"199",
"223",
"227",
"229",
"277",
"283",
"317",
"397",
"433",
"521",
"541",
"577",
"607",
"677",
"743",
"757",
"811",
"863",
"881",
"911",
"971",
"1031",
"1049",
"1063",
"1093",
"1249",
"1319",
"1373",
"1433",
"1489"
]
| [
"nonn"
]
| 35 | 1 | 1 | [
"A001065",
"A048138",
"A064440",
"A238895",
"A238896",
"A356445"
]
| null | Amiram Eldar, Sep 23 2022 | 2022-09-24T07:14:51 | oeisdata/seq/A356/A356445.seq | 1c4528f8c727085d766a55a0e4f16ccd |
A356446 | Number of permutations f of {1,...,n} with f(1) = 2 and f(2) = 1 such that the numbers f(k)*f(k+1) (0 < k < n) are distinct and Sum_{k=1..n-1} 1/(f(k)*f(k+1)) = 1. | [
"0",
"0",
"0",
"0",
"1",
"1",
"1",
"1",
"2",
"1",
"11",
"7",
"61",
"388",
"2933",
"2741"
]
| [
"nonn",
"more"
]
| 18 | 2 | 9 | [
"A000961",
"A322069",
"A322070",
"A356187",
"A356446"
]
| null | Zhi-Wei Sun, Aug 07 2022 | 2022-08-20T08:50:30 | oeisdata/seq/A356/A356446.seq | 7fed10849ca36ad3afe13cacce9e72f9 |
A356447 | Integers k such that (k+1)*(2*k-1) does not divide the central binomial coefficient B(k) = binomial(2*k,k) = A000984(k). | [
"2",
"5",
"8",
"11",
"14",
"26",
"29",
"32",
"35",
"38",
"41",
"80",
"83",
"86",
"89",
"92",
"95",
"107",
"110",
"113",
"116",
"119",
"122",
"242",
"245",
"248",
"251",
"254",
"257",
"269",
"272",
"275",
"278",
"281",
"284",
"323",
"326",
"329",
"332",
"335",
"338",
"350",
"353",
"356",
"359",
"362",
"365",
"728",
"731",
"734",
"737",
"740",
"743",
"755",
"758",
"761"
]
| [
"nonn",
"easy"
]
| 59 | 1 | 1 | [
"A000108",
"A000984",
"A073076",
"A096304",
"A356447"
]
| null | Valerio De Angelis, Aug 07 2022 | 2022-10-02T01:30:38 | oeisdata/seq/A356/A356447.seq | defc68a5f36754c97b3ea13c6cfaf477 |
A356448 | Even numbers k such that k^2 is in A014567. | [
"2",
"4",
"6",
"8",
"10",
"12",
"16",
"18",
"20",
"22",
"24",
"26",
"28",
"30",
"32",
"34",
"36",
"38",
"40",
"44",
"46",
"48",
"50",
"52",
"54",
"56",
"58",
"60",
"62",
"64",
"66",
"68",
"72",
"74",
"76",
"80",
"82",
"86",
"88",
"90",
"92",
"94",
"96",
"100",
"102",
"104",
"106",
"108",
"110",
"116",
"118",
"120",
"122",
"128",
"130",
"132",
"134",
"136",
"138",
"140",
"142",
"144",
"146",
"148"
]
| [
"nonn",
"easy"
]
| 13 | 1 | 1 | [
"A000203",
"A014567",
"A356382",
"A356448",
"A356449",
"A356451",
"A356452"
]
| null | Jianing Song, Aug 07 2022 | 2022-08-08T09:15:17 | oeisdata/seq/A356/A356448.seq | 0dd06efd5c8a60a3177bec812d65db1a |
A356449 | Numbers k such that 2*k^2 is in A014567. | [
"1",
"2",
"4",
"5",
"7",
"8",
"11",
"13",
"14",
"16",
"17",
"19",
"20",
"22",
"23",
"25",
"26",
"29",
"31",
"32",
"34",
"35",
"37",
"38",
"41",
"43",
"44",
"46",
"47",
"49",
"52",
"53",
"55",
"56",
"58",
"59",
"61",
"62",
"64",
"65",
"67",
"68",
"71",
"73",
"74",
"76",
"79",
"80",
"82",
"83",
"85",
"86",
"88",
"89",
"91",
"92",
"94",
"95",
"97",
"98",
"100",
"101",
"103",
"104",
"106",
"107",
"109",
"112",
"113"
]
| [
"nonn",
"easy"
]
| 16 | 1 | 2 | [
"A000203",
"A014567",
"A065766",
"A356382",
"A356448",
"A356449",
"A356451",
"A356453"
]
| null | Jianing Song, Aug 07 2022 | 2022-08-08T09:15:33 | oeisdata/seq/A356/A356449.seq | cf11b56e0a09f749275985a12120afbd |
A356450 | Positions of numbers m = A005940(n+1) such that m < n. | [
"8",
"16",
"17",
"32",
"33",
"34",
"35",
"64",
"65",
"66",
"67",
"68",
"69",
"71",
"128",
"129",
"130",
"131",
"132",
"133",
"134",
"135",
"136",
"137",
"139",
"143",
"256",
"257",
"258",
"259",
"260",
"261",
"262",
"263",
"264",
"265",
"266",
"267",
"269",
"271",
"272",
"273",
"275",
"279",
"287",
"288",
"384",
"512",
"513",
"514",
"515",
"516",
"517",
"518",
"519",
"520"
]
| [
"nonn"
]
| 14 | 1 | 1 | [
"A005940",
"A029747",
"A356450",
"A356455"
]
| null | Michael De Vlieger, Aug 07 2022 | 2023-08-16T21:14:47 | oeisdata/seq/A356/A356450.seq | 515f5a02ff0d7dca8d1051499c0f9b07 |
A356451 | Numbers k such that 4*k^2 is in A014567. | [
"1",
"2",
"3",
"4",
"5",
"6",
"8",
"9",
"10",
"11",
"12",
"13",
"14",
"15",
"16",
"17",
"18",
"19",
"20",
"22",
"23",
"24",
"25",
"26",
"27",
"28",
"29",
"30",
"31",
"32",
"33",
"34",
"36",
"37",
"38",
"40",
"41",
"43",
"44",
"45",
"46",
"47",
"48",
"50",
"51",
"52",
"53",
"54",
"55",
"58",
"59",
"60",
"61",
"64",
"65",
"66",
"67",
"68",
"69",
"70",
"71",
"72",
"73",
"74",
"75",
"76",
"79",
"80",
"81",
"82",
"83"
]
| [
"nonn",
"easy"
]
| 12 | 1 | 2 | [
"A000203",
"A014567",
"A356382",
"A356448",
"A356449",
"A356451",
"A356454"
]
| null | Jianing Song, Aug 07 2022 | 2022-08-08T09:15:21 | oeisdata/seq/A356/A356451.seq | e86c14d125b5712781efd14f58138668 |
A356452 | Even numbers k such that k^2 is not in A014567; complement of A356448 in the even numbers. | [
"14",
"42",
"70",
"78",
"84",
"98",
"112",
"114",
"124",
"126",
"154",
"156",
"168",
"182",
"186",
"198",
"210",
"222",
"228",
"234",
"238",
"252",
"258",
"266",
"294",
"308",
"310",
"312",
"322",
"336",
"342",
"350",
"366",
"372",
"378",
"390",
"396",
"402",
"406",
"418",
"420",
"434",
"438",
"444",
"456",
"462",
"468",
"474",
"490",
"504",
"516",
"518",
"532",
"546",
"550",
"558"
]
| [
"nonn",
"easy"
]
| 13 | 1 | 1 | [
"A000203",
"A014567",
"A356448",
"A356452",
"A356453",
"A356454"
]
| null | Jianing Song, Aug 07 2022 | 2023-03-09T15:34:25 | oeisdata/seq/A356/A356452.seq | c613b0a54371d20878aea83b2abddc1c |
A356453 | Numbers k such that 2*k^2 is not in A014567; complement of A356449. | [
"3",
"6",
"9",
"10",
"12",
"15",
"18",
"21",
"24",
"27",
"28",
"30",
"33",
"36",
"39",
"40",
"42",
"45",
"48",
"50",
"51",
"54",
"57",
"60",
"63",
"66",
"69",
"70",
"72",
"75",
"77",
"78",
"81",
"84",
"87",
"90",
"93",
"96",
"99",
"102",
"105",
"108",
"110",
"111",
"114",
"117",
"120",
"123",
"126",
"129",
"130",
"132",
"133",
"135",
"136",
"138",
"140",
"141",
"144",
"147",
"150",
"153",
"154",
"155"
]
| [
"nonn",
"easy"
]
| 21 | 1 | 1 | [
"A000203",
"A014567",
"A065766",
"A356448",
"A356449",
"A356452",
"A356453",
"A356454",
"A356456"
]
| null | Jianing Song, Aug 07 2022 | 2024-08-07T14:11:12 | oeisdata/seq/A356/A356453.seq | d2fd00e9480c38f0446e10d94b9406d2 |
A356454 | Numbers k such that 4*k^2 is not in A014567; complement of A356451. | [
"7",
"21",
"35",
"39",
"42",
"49",
"56",
"57",
"62",
"63",
"77",
"78",
"84",
"91",
"93",
"99",
"105",
"111",
"114",
"117",
"119",
"126",
"129",
"133",
"147",
"154",
"155",
"156",
"161",
"168",
"171",
"175",
"183",
"186",
"189",
"195",
"198",
"201",
"203",
"209",
"210",
"217",
"219",
"222",
"228",
"231",
"234",
"237",
"245",
"252",
"258",
"259",
"266",
"273",
"275",
"279",
"280",
"285"
]
| [
"nonn",
"easy"
]
| 9 | 1 | 1 | [
"A000203",
"A014567",
"A356448",
"A356452",
"A356453",
"A356454"
]
| null | Jianing Song, Aug 07 2022 | 2022-08-08T09:15:39 | oeisdata/seq/A356/A356454.seq | e33568e407dab5a9dcef487ac2970caf |
A356455 | Numbers m = A005940(n) such that A005940(n) < (n-1), listed in order of appearance in A005940. | [
"7",
"11",
"14",
"13",
"22",
"33",
"28",
"17",
"26",
"39",
"44",
"65",
"66",
"56",
"19",
"34",
"51",
"52",
"85",
"78",
"117",
"88",
"119",
"130",
"132",
"112",
"23",
"38",
"57",
"68",
"95",
"102",
"153",
"104",
"133",
"170",
"255",
"156",
"234",
"176",
"209",
"238",
"260",
"264",
"224",
"247",
"361",
"29",
"46",
"69",
"76",
"115",
"114",
"171",
"136",
"161",
"190",
"285",
"204"
]
| [
"nonn"
]
| 9 | 1 | 1 | [
"A005940",
"A029747",
"A356450",
"A356455"
]
| null | Michael De Vlieger, Aug 07 2022 | 2022-08-09T02:04:45 | oeisdata/seq/A356/A356455.seq | f0eb8ce91274ef02c9fff7c60f63bbb4 |
A356456 | Numbers k not divisible by 3 such that 2*k^2 is not in A014567. | [
"10",
"28",
"40",
"50",
"70",
"77",
"110",
"130",
"133",
"136",
"140",
"154",
"155",
"160",
"161",
"170",
"176",
"190",
"196",
"200",
"209",
"224",
"230",
"250",
"259",
"266",
"275",
"280",
"290",
"308",
"310",
"322",
"350",
"364",
"370",
"371",
"377",
"385",
"410",
"416",
"418",
"430",
"440",
"469",
"470",
"476",
"490",
"496",
"518",
"520",
"530",
"532",
"539",
"550",
"553",
"590"
]
| [
"nonn",
"easy"
]
| 11 | 1 | 1 | [
"A000203",
"A008585",
"A014567",
"A065766",
"A356453",
"A356456"
]
| null | Jianing Song, Aug 07 2022 | 2022-08-08T09:15:43 | oeisdata/seq/A356/A356456.seq | a822870c954d132c8d30a072d60ef430 |
A356457 | a(n) is the least number that can be written in exactly n ways as p*q + q*r + p*r where (p,q,r) is an unordered triple of distinct primes. | [
"1",
"31",
"71",
"151",
"191",
"491",
"671",
"887",
"311",
"1151",
"1391",
"1751",
"1031",
"2711",
"2831",
"3911",
"1991",
"3191",
"5351",
"9551",
"7031",
"20951",
"8951",
"8711",
"10631",
"5591",
"15431",
"10391",
"15791",
"28031",
"20471",
"17111",
"48191",
"27191",
"31391",
"39191",
"52631",
"35591",
"42311",
"61871",
"50951",
"92231",
"70391",
"108071",
"99431",
"103991",
"96071"
]
| [
"nonn"
]
| 14 | 0 | 2 | [
"A003415",
"A007304",
"A087053",
"A356457"
]
| null | J. M. Bergot and Robert Israel, Aug 07 2022 | 2022-08-14T10:20:18 | oeisdata/seq/A356/A356457.seq | 85b3b8dfce49fa5de8cc3ae6deb2afb9 |
A356458 | Expansion of e.g.f. ( Product_{k>0} B(x^k) )^(1/(1-x)) where B(x) = exp(exp(x)-1) = e.g.f. of Bell numbers. | [
"1",
"1",
"6",
"38",
"319",
"3117",
"36359",
"476121",
"7025708",
"114118746",
"2029450055",
"39078892305",
"810834093733",
"17998186069489",
"425672049713174",
"10676653292086790",
"283014906314277059",
"7901659174554937925",
"231719030698518379003",
"7118469816302381503209"
]
| [
"nonn"
]
| 13 | 0 | 3 | [
"A000110",
"A209903",
"A355886",
"A356025",
"A356458",
"A356461"
]
| null | Seiichi Manyama, Aug 08 2022 | 2022-08-08T09:39:49 | oeisdata/seq/A356/A356458.seq | 1427bfc9e04f15db1f2ab2b14ee9264f |
A356459 | a(n) = n! * Sum_{k=1..n} Sum_{d|k} d/(k/d)!. | [
"1",
"7",
"40",
"281",
"2006",
"17677",
"159020",
"1678721",
"18555850",
"230978981",
"2979853592",
"43323807265",
"644160764846",
"10543905398405",
"178896116995276",
"3284281839169217",
"61879477543508690",
"1264313089711322821",
"26333205612282941600",
"588074615109602665601"
]
| [
"nonn"
]
| 9 | 1 | 2 | [
"A354863",
"A355886",
"A356009",
"A356459"
]
| null | Seiichi Manyama, Aug 08 2022 | 2022-08-08T09:39:53 | oeisdata/seq/A356/A356459.seq | ea238728b96de606e13cb7ed30c22ef2 |
A356460 | Expansion of e.g.f. Product_{k>0} B(x^k)^k where B(x) = exp(exp(x)-1) = e.g.f. of Bell numbers. | [
"1",
"1",
"6",
"35",
"303",
"2772",
"32903",
"410335",
"6051692",
"95183187",
"1675869175",
"31437027030",
"644157830077",
"13976891765137",
"325719071472590",
"8007861177420275",
"208953947981129027",
"5725964099963426924",
"165258064179632753563",
"4987477844227598529047"
]
| [
"nonn"
]
| 15 | 0 | 3 | [
"A000110",
"A209902",
"A209903",
"A354863",
"A356460",
"A356461"
]
| null | Seiichi Manyama, Aug 08 2022 | 2022-08-09T11:19:08 | oeisdata/seq/A356/A356460.seq | 9b2c84cdd5ad68378c6ad46dbcf0dd67 |
A356461 | Expansion of e.g.f. ( Product_{k>0} B(x^k)^k )^(1/(1-x)) where B(x) = exp(exp(x)-1) = e.g.f. of Bell numbers. | [
"1",
"1",
"8",
"62",
"631",
"7417",
"104489",
"1648845",
"29319588",
"572982162",
"12250559615",
"283321630605",
"7053444523393",
"187711377451249",
"5317981377046420",
"159652557864884330",
"5061465465801168419",
"168886786171198864725",
"5914650120884760212977",
"216844308186908733542877"
]
| [
"nonn"
]
| 10 | 0 | 3 | [
"A000110",
"A356025",
"A356458",
"A356459",
"A356460",
"A356461"
]
| null | Seiichi Manyama, Aug 08 2022 | 2022-08-08T09:40:03 | oeisdata/seq/A356/A356461.seq | 6ab4c238862447e3bc90d2d3211cd9dd |
A356462 | a(n) is the maximum number of Z x Z lattice points inside or on a circle of radius n^(1/2) for any position of the center of the circle. | [
"1",
"5",
"9",
"12",
"14",
"21",
"21",
"24",
"28",
"32",
"37",
"37",
"41",
"45",
"48",
"52",
"52",
"57",
"61",
"63",
"69",
"69",
"72",
"76",
"78",
"81",
"89",
"89",
"92",
"97",
"97",
"100",
"104",
"112",
"112",
"115",
"116",
"121",
"122",
"127",
"129",
"137",
"137",
"140",
"144",
"148",
"148",
"152",
"155",
"157",
"161",
"164",
"169",
"177",
"177"
]
| [
"nonn"
]
| 22 | 0 | 2 | [
"A057655",
"A123690",
"A346993",
"A356462"
]
| null | Bernard Montaron, Aug 08 2022 | 2025-02-17T08:30:13 | oeisdata/seq/A356/A356462.seq | c11825a134188a897927ced8bbd467e5 |
A356463 | Sum of powers of roots of x^3 - 4*x^2 + x + 1. | [
"3",
"4",
"14",
"49",
"178",
"649",
"2369",
"8649",
"31578",
"115294",
"420949",
"1536924",
"5611453",
"20487939",
"74803379",
"273114124",
"997165178",
"3640743209",
"13292693534",
"48532865749",
"177198026253",
"646966545729",
"2362135290914"
]
| [
"nonn",
"easy"
]
| 22 | 0 | 1 | [
"A052941",
"A356463"
]
| null | Greg Dresden and Ding Hao, Aug 08 2022 | 2022-09-13T09:36:48 | oeisdata/seq/A356/A356463.seq | 9d72906f71f60fe8b9f84bafbab2ac01 |
A356464 | Number of black keys in each group of black keys on a standard 88-key piano (left to right). | [
"1",
"2",
"3",
"2",
"3",
"2",
"3",
"2",
"3",
"2",
"3",
"2",
"3",
"2",
"3"
]
| [
"easy",
"fini",
"full",
"nonn"
]
| 37 | 1 | 2 | [
"A059620",
"A060106",
"A060107",
"A081031",
"A081032",
"A329207",
"A356464"
]
| null | Peter Woodward, Aug 08 2022 | 2022-08-20T09:00:46 | oeisdata/seq/A356/A356464.seq | 205487359b5be551e4612461563dcbce |
A356465 | The number of unit squares enclosed by the rectangular spiral of which the n-th side has length prime(n). | [
"0",
"2",
"6",
"12",
"27",
"59",
"113",
"179",
"257",
"359",
"497",
"747",
"963",
"1227",
"1577",
"1799",
"2081",
"2611",
"3223",
"3663",
"4167",
"4817",
"5231",
"5847",
"6657",
"7527",
"8801",
"9869",
"10439",
"11057",
"11699",
"12425",
"14675",
"16817",
"18027",
"19139",
"20855",
"22595",
"23803",
"25711",
"27321",
"29011",
"31063",
"32495"
]
| [
"nonn"
]
| 25 | 0 | 2 | [
"A000040",
"A356465"
]
| null | Bob Andriesse, Aug 08 2022 | 2022-10-23T22:57:45 | oeisdata/seq/A356/A356465.seq | 8208034b9fc18f12d60025b255b2635f |
A356466 | Prime numbers in the sublists defined in A348168 that contain exactly two primes. | [
"11",
"13",
"17",
"19",
"29",
"31",
"59",
"61",
"79",
"83",
"127",
"131",
"137",
"139",
"149",
"151",
"163",
"167",
"179",
"181",
"191",
"193",
"197",
"199",
"239",
"241",
"331",
"337",
"347",
"349",
"397",
"401",
"419",
"421",
"431",
"433",
"439",
"443",
"521",
"523",
"541",
"547",
"673",
"677",
"701",
"709",
"787",
"797",
"809",
"811",
"821",
"823",
"827",
"829"
]
| [
"nonn"
]
| 10 | 1 | 1 | [
"A348168",
"A356466"
]
| null | Ya-Ping Lu, Aug 08 2022 | 2024-04-25T13:53:45 | oeisdata/seq/A356/A356466.seq | 911f88fe65ab6c8f2f28db74a010ce93 |
A356467 | Smallest prime congruent to 1 (mod prime(n)) which is the norm of some principal ideal in the ring of prime(n)-th cyclotomic integers. | [
"7",
"11",
"29",
"23",
"53",
"103",
"191",
"599",
"4931",
"5953",
"32783",
"101107",
"178021",
"549149"
]
| [
"nonn",
"more"
]
| 11 | 2 | 1 | [
"A035095",
"A356467"
]
| null | Paul Vanderveen, Aug 08 2022 | 2023-07-15T10:36:23 | oeisdata/seq/A356/A356467.seq | 0eb8efd1febf06f3d219441ab2ad1100 |
A356468 | Yu. V. Matiyasevich's Riemann Hypothesis test. | [
"1",
"10",
"143",
"1221",
"21249",
"274815",
"5639631",
"90945117",
"1826620833",
"38618333559",
"1129082889375",
"28218286333125",
"915660945621585",
"26435665650141135",
"888640364800590255",
"28827658089741286125",
"1176745390297425986625",
"43482016069074330150375",
"1949108731388102309925375"
]
| [
"nonn"
]
| 12 | 1 | 2 | [
"A000720",
"A356468"
]
| null | Peter Luschny, Aug 08 2022 | 2023-08-25T17:20:51 | oeisdata/seq/A356/A356468.seq | 163fc3886614fe7ed2e18b6d9de14814 |
A356469 | a(n) = [(n + 1)/(1 - 1/r)] - [n - n/r] where r = sqrt(2) and [] denotes the floor function. | [
"3",
"6",
"10",
"13",
"16",
"19",
"22",
"25",
"28",
"32",
"35",
"37",
"41",
"44",
"47",
"50",
"54",
"57",
"59",
"63",
"66",
"69",
"72",
"75",
"78",
"81",
"85",
"88",
"91",
"94",
"97",
"100",
"103",
"107",
"110",
"112",
"116",
"119",
"122",
"125",
"128",
"131",
"134",
"138",
"141",
"144",
"147",
"150",
"153",
"156",
"160",
"163",
"165",
"169",
"172",
"175",
"178",
"182",
"185"
]
| [
"nonn"
]
| 4 | 0 | 1 | [
"A285684",
"A356469"
]
| null | Peter Luschny, Aug 31 2022 | 2022-08-31T13:30:36 | oeisdata/seq/A356/A356469.seq | 8e03584dd5d19edde8bb610aca5b3851 |
A356470 | Decimal expansion of (3 - sqrt(5))/(2*sqrt(2)). | [
"2",
"7",
"0",
"0",
"9",
"0",
"7",
"5",
"6",
"7",
"3",
"7",
"7",
"2",
"6",
"4",
"5",
"3",
"6",
"0",
"1",
"5",
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"3",
"1",
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"0",
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"9",
"0",
"9",
"3",
"9",
"2",
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"4",
"9",
"7",
"3",
"6",
"5",
"1",
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"1",
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"1",
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"1",
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"3",
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"2",
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"4",
"9",
"0",
"0",
"7",
"4",
"9",
"1",
"8",
"6",
"7",
"7",
"0",
"7",
"2",
"3",
"8",
"0",
"1",
"7",
"2",
"8",
"6",
"2"
]
| [
"nonn",
"cons"
]
| 20 | 0 | 1 | [
"A002193",
"A356470"
]
| null | Andrew Slattery, Aug 08 2022 | 2023-08-21T12:16:15 | oeisdata/seq/A356/A356470.seq | aa9caceaf120cfc55ec0473f5b3048e3 |
A356471 | First of 5 consecutive primes p,q,r,s,t such that p*q+ q*r + r*s + s*t + t*p is prime. | [
"19",
"41",
"47",
"53",
"157",
"199",
"491",
"557",
"563",
"571",
"647",
"1063",
"1091",
"1097",
"1109",
"1163",
"1171",
"1217",
"1259",
"1279",
"1361",
"1367",
"1487",
"1601",
"1621",
"1753",
"1901",
"1951",
"2053",
"2161",
"2383",
"2441",
"2549",
"2777",
"2851",
"2879",
"2887",
"2953",
"2957",
"3041",
"3061",
"3067",
"3163",
"3191",
"3491",
"3499",
"3719",
"3881",
"4003",
"4007",
"4013",
"4093"
]
| [
"nonn"
]
| 16 | 1 | 1 | [
"A356471",
"A356475",
"A356477"
]
| null | J. M. Bergot and Robert Israel, Aug 08 2022 | 2022-09-03T08:07:03 | oeisdata/seq/A356/A356471.seq | e673b2e455256b531763debca976e054 |
A356472 | Numerator of the average of gcd(i,n) for i = 1..n. | [
"1",
"3",
"5",
"2",
"9",
"5",
"13",
"5",
"7",
"27",
"21",
"10",
"25",
"39",
"3",
"3",
"33",
"7",
"37",
"18",
"65",
"63",
"45",
"25",
"13",
"75",
"3",
"26",
"57",
"9",
"61",
"7",
"35",
"99",
"117",
"14",
"73",
"111",
"125",
"9",
"81",
"65",
"85",
"42",
"21",
"135",
"93",
"5",
"19",
"39",
"55",
"50",
"105",
"9",
"189",
"65",
"185",
"171",
"117",
"6",
"121",
"183",
"13",
"4",
"45",
"105",
"133",
"66",
"75",
"351",
"141",
"35",
"145",
"219",
"13",
"74",
"39",
"125",
"157"
]
| [
"easy",
"frac",
"nonn"
]
| 51 | 1 | 2 | [
"A001620",
"A013661",
"A018804",
"A057661",
"A306016",
"A356472",
"A356473"
]
| null | Matthias Kaak, Aug 08 2022 | 2024-12-25T05:34:19 | oeisdata/seq/A356/A356472.seq | 4b7ddb76900040a0284fc33e28c45821 |
A356473 | Denominator of the average of gcd(i,n) for i = 1..n. | [
"1",
"2",
"3",
"1",
"5",
"2",
"7",
"2",
"3",
"10",
"11",
"3",
"13",
"14",
"1",
"1",
"17",
"2",
"19",
"5",
"21",
"22",
"23",
"6",
"5",
"26",
"1",
"7",
"29",
"2",
"31",
"2",
"11",
"34",
"35",
"3",
"37",
"38",
"39",
"2",
"41",
"14",
"43",
"11",
"5",
"46",
"47",
"1",
"7",
"10",
"17",
"13",
"53",
"2",
"55",
"14",
"57",
"58",
"59",
"1",
"61",
"62",
"3",
"1",
"13",
"22",
"67",
"17",
"23",
"70",
"71",
"6",
"73",
"74",
"3",
"19",
"11",
"26",
"79",
"5",
"3",
"82",
"83",
"21",
"85",
"86",
"29"
]
| [
"easy",
"frac",
"nonn",
"look"
]
| 50 | 1 | 2 | [
"A018804",
"A356472",
"A356473"
]
| null | Matthias Kaak, Aug 08 2022 | 2023-04-28T08:16:52 | oeisdata/seq/A356/A356473.seq | 8fc4ba40d9321adcbed7199dd0272d1e |
A356474 | a(n) = phi(rad(prime(n)-1)), where phi = A000010 and rad = A007947. | [
"1",
"1",
"1",
"2",
"4",
"2",
"1",
"2",
"10",
"6",
"8",
"2",
"4",
"12",
"22",
"12",
"28",
"8",
"20",
"24",
"2",
"24",
"40",
"10",
"2",
"4",
"32",
"52",
"2",
"6",
"12",
"48",
"16",
"44",
"36",
"8",
"24",
"2",
"82",
"42",
"88",
"8",
"72",
"2",
"6",
"20",
"48",
"72",
"112",
"36",
"28",
"96",
"8",
"4",
"1",
"130",
"66",
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"44",
"24",
"92",
"72",
"32",
"120",
"24",
"78",
"80",
"12",
"172",
"56",
"10",
"178",
"120",
"60"
]
| [
"nonn",
"easy"
]
| 24 | 1 | 4 | [
"A000010",
"A007947",
"A077063",
"A173557",
"A356474"
]
| null | Jianing Song, Aug 09 2022 | 2022-08-09T09:02:16 | oeisdata/seq/A356/A356474.seq | 64e97280130875c109390d5f5d953ded |
A356475 | First of three consecutive primes p,q,r such that p*q + q*r + r*p is prime. | [
"2",
"3",
"5",
"7",
"17",
"29",
"37",
"41",
"43",
"67",
"83",
"103",
"137",
"157",
"179",
"181",
"193",
"227",
"277",
"283",
"347",
"359",
"383",
"431",
"457",
"461",
"607",
"661",
"701",
"709",
"757",
"773",
"823",
"827",
"839",
"859",
"937",
"967",
"1013",
"1051",
"1061",
"1109",
"1129",
"1187",
"1201",
"1213",
"1249",
"1283",
"1307",
"1327",
"1373",
"1423",
"1439",
"1471",
"1481",
"1487",
"1543",
"1567"
]
| [
"nonn"
]
| 17 | 1 | 1 | [
"A189759",
"A356471",
"A356475",
"A356477"
]
| null | J. M. Bergot and Robert Israel, Aug 08 2022 | 2022-09-06T10:54:16 | oeisdata/seq/A356/A356475.seq | f17a94e4cda549cac13cbea59e77c623 |
A356476 | Decimal expansion of Loschmidt constant in m^-3 (273.15 K, 100 kPa). | [
"2",
"6",
"5",
"1",
"6",
"4",
"5",
"8",
"0",
"4",
"8",
"8",
"3",
"7",
"3",
"4",
"3",
"4",
"2",
"4",
"1",
"1",
"2",
"0",
"4",
"6",
"9",
"5",
"2",
"3",
"5",
"4",
"9",
"7",
"7",
"7",
"2",
"9",
"9",
"0",
"2",
"7",
"9",
"0",
"0",
"6",
"6",
"8",
"4",
"6",
"8",
"3",
"3",
"2",
"9",
"7",
"7",
"2",
"5",
"1",
"1",
"1",
"0",
"2",
"2",
"1",
"4",
"6",
"0",
"0",
"7",
"8",
"7",
"6",
"0",
"3",
"7",
"4",
"2",
"8",
"5",
"6",
"2",
"3",
"0",
"7",
"0",
"2",
"3",
"5",
"0",
"1",
"7",
"3",
"4",
"4",
"4"
]
| [
"nonn",
"cons",
"easy"
]
| 17 | 26 | 1 | [
"A070063",
"A070064",
"A228163",
"A322578",
"A356476"
]
| null | Christoph B. Kassir, Aug 08 2022 | 2022-09-18T12:35:02 | oeisdata/seq/A356/A356476.seq | 84319ca02e1a08d8ef488d6ad8d37b6f |
A356477 | a(n) is the start of the first sequence of 2*n+1 consecutive primes p_1, p_2, ..., p_(2*n+1) such that p_1*p_2 + p_2*p_3 + ... + p_(2*n)*p_(2*n+1) + p_(2*n+1)*p_1 is prime. | [
"2",
"19",
"19",
"2",
"23",
"2",
"7",
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"2",
"5",
"113",
"5",
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"13",
"67",
"53",
"11",
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"23",
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"43",
"13",
"19",
"2",
"59",
"7",
"29",
"113",
"13",
"5",
"11"
]
| [
"nonn"
]
| 16 | 1 | 1 | [
"A070934",
"A356471",
"A356475",
"A356477"
]
| null | J. M. Bergot and Robert Israel, Aug 08 2022 | 2022-09-04T12:51:22 | oeisdata/seq/A356/A356477.seq | 5c0545ac13c32b45b7fe135fb7bad802 |
A356478 | a(n) is the least k such that there are exactly n primes p <= k such that 2*k-p and p*(2*k-p)+2*k are also prime. | [
"2",
"4",
"11",
"15",
"21",
"35",
"42",
"111",
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"126",
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"3252",
"2622",
"2940",
"1575",
"2310",
"2541",
"3987",
"2772"
]
| [
"nonn"
]
| 58 | 0 | 1 | [
"A072511",
"A356478",
"A356864"
]
| null | J. M. Bergot and Robert Israel, Sep 01 2022 | 2022-09-05T09:10:42 | oeisdata/seq/A356/A356478.seq | fd4783475c8f0fd87e776805031b4b2f |
A356479 | Decimal expansion of (sqrt(3)/Pi) * sinh(Pi/sqrt(3)). | [
"1",
"6",
"4",
"5",
"9",
"0",
"2",
"5",
"1",
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"9",
"7",
"4",
"8",
"9",
"4",
"8",
"9",
"0",
"6",
"5",
"7"
]
| [
"nonn",
"cons"
]
| 37 | 1 | 2 | [
"A000796",
"A002194",
"A334401",
"A356479"
]
| null | Christoph B. Kassir, Aug 08 2022 | 2022-08-13T15:57:29 | oeisdata/seq/A356/A356479.seq | a7d4acb13e587775cb075184bfd7d6b1 |
A356480 | a(n) is the minimal number of river crossings necessary to solve the missionaries and cannibals problem for n missionaries and n cannibals where the boat capacity is the minimum necessary to allow a solution. | [
"1",
"5",
"11",
"9",
"11",
"9",
"11",
"13",
"15",
"17",
"19",
"21",
"23",
"25",
"27",
"29",
"31",
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"125",
"127",
"129",
"131",
"133",
"135"
]
| [
"nonn",
"easy"
]
| 75 | 1 | 2 | [
"A060747",
"A167484",
"A356480"
]
| null | Sela Fried, Aug 09 2022 | 2022-08-20T06:25:48 | oeisdata/seq/A356/A356480.seq | 8d4efa141e4b769c5c822e5949034e60 |
A356481 | a(n) is the hafnian of a symmetric Toeplitz matrix M(2*n) whose first row consists of 1, 2, ..., 2*n. | [
"1",
"2",
"21",
"532",
"24845",
"1856094",
"203076097",
"30633787976",
"6097546660185",
"1548899852221210",
"489114616743840461"
]
| [
"nonn",
"hard",
"more"
]
| 18 | 0 | 2 | [
"A001792",
"A202038",
"A204235",
"A336114",
"A336286",
"A336400",
"A338456",
"A356481",
"A356482",
"A356483",
"A356484"
]
| null | Stefano Spezia, Aug 09 2022 | 2023-10-14T23:54:18 | oeisdata/seq/A356/A356481.seq | 67d2c905c92e59e49223fac646bc1745 |
A356482 | a(n) is the hafnian of a symmetric Toeplitz matrix M(2*n) whose first row consists of 2*n, 2*n-1, ..., 1. | [
"1",
"1",
"16",
"714",
"62528",
"9056720",
"1960138560",
"592615689904",
"238560786221056",
"123358665203311104",
"79683847063011614720"
]
| [
"nonn",
"hard",
"more"
]
| 14 | 0 | 3 | [
"A001792",
"A202038",
"A307783",
"A336114",
"A336286",
"A336400",
"A338456",
"A356481",
"A356482",
"A356483",
"A356484"
]
| null | Stefano Spezia, Aug 09 2022 | 2023-10-14T23:54:27 | oeisdata/seq/A356/A356482.seq | 90f8164b595bc6bc9d685dc24b9d704c |
A356483 | a(n) is the hafnian of a symmetric Toeplitz matrix M(2*n) whose first row consists of prime(1), prime(2), ..., prime(2*n). | [
"1",
"3",
"55",
"2999",
"347391",
"69702479",
"22441691645",
"10776262328919",
"7190279422736061",
"6439969796874334809",
"7447188585071730451961"
]
| [
"nonn",
"hard",
"more"
]
| 16 | 0 | 2 | [
"A202038",
"A336114",
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"A336400",
"A338456",
"A356481",
"A356482",
"A356483",
"A356484",
"A356490",
"A356491"
]
| null | Stefano Spezia, Aug 09 2022 | 2023-10-14T23:54:38 | oeisdata/seq/A356/A356483.seq | e69e1b3a0005f49fd53142d270068217 |
A356484 | a(n) is the hafnian of a symmetric Toeplitz matrix M(2*n) whose first row consists of prime(2*n), prime(2*n-1), ..., prime(1). | [
"1",
"2",
"44",
"5210",
"1368900",
"604109562",
"535920536336",
"728155179271474",
"1103827431509790216",
"2651375713654260218986",
"7537958658258053003685636"
]
| [
"nonn",
"hard",
"more"
]
| 25 | 0 | 2 | [
"A202038",
"A336114",
"A336286",
"A336400",
"A338456",
"A356481",
"A356482",
"A356483",
"A356484",
"A356492",
"A356493"
]
| null | Stefano Spezia, Aug 09 2022 | 2023-10-14T23:54:50 | oeisdata/seq/A356/A356484.seq | cf1fef83c5324e99ee0249d22643769b |
A356485 | a(n) = n! * Sum_{k=1..n} A000010(k)/k. | [
"1",
"3",
"13",
"64",
"416",
"2736",
"23472",
"207936",
"2113344",
"22584960",
"284722560",
"3576337920",
"52240412160",
"768727895040",
"12228344755200",
"206114911027200",
"3838718125670400",
"71231050830643200",
"1468632692485324800",
"30345814652977152000",
"666456931810639872000",
"15172961921551171584000"
]
| [
"nonn"
]
| 11 | 1 | 2 | [
"A000010",
"A002088",
"A011755",
"A356010",
"A356297",
"A356298",
"A356323",
"A356485"
]
| null | Vaclav Kotesovec, Aug 09 2022 | 2025-02-16T08:34:03 | oeisdata/seq/A356/A356485.seq | 9f6b45e8d6a9331ed0318fecfcdf9839 |
A356486 | a(n) = (n-1)! * Sum_{d|n} d^n / (d-1)!. | [
"1",
"5",
"29",
"358",
"3149",
"98196",
"824263",
"73122736",
"784270089",
"158028202000",
"285315299411",
"855386690484096",
"302875585593853",
"5876921233326141376",
"111916280261483009775",
"73985874496557113890816",
"827240282809126652177",
"1625215094103508198780449024"
]
| [
"nonn"
]
| 17 | 1 | 2 | [
"A087906",
"A354890",
"A356486",
"A356487"
]
| null | Seiichi Manyama, Aug 09 2022 | 2023-08-30T02:00:40 | oeisdata/seq/A356/A356486.seq | d2369e3159205bacb6533384c35678e3 |
A356487 | Expansion of e.g.f. Product_{k>0} 1/(1 - (k * x)^k)^(1/k!). | [
"1",
"1",
"6",
"45",
"580",
"7105",
"170076",
"2654575",
"116426528",
"2386183761",
"209503380160",
"3455683548691",
"969334978024920",
"15164681616944353",
"6510178188269825720",
"223847763757748796975",
"81261936394687862700256",
"1581790511799886415713825"
]
| [
"nonn"
]
| 12 | 0 | 3 | [
"A023882",
"A209902",
"A356486",
"A356487"
]
| null | Seiichi Manyama, Aug 09 2022 | 2022-08-09T11:20:01 | oeisdata/seq/A356/A356487.seq | 7def72d260bd32af278c1bbe53483b5a |
A356488 | Numbers k such that the equation x^2 - k*y^4 = -1 has a solution for which |y| > 2. | [
"2",
"53",
"314",
"1042",
"1685",
"1825",
"3281",
"4586",
"5521",
"6770",
"8597",
"9050",
"11509",
"13858",
"17498",
"20369",
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"28085",
"28130",
"29041",
"31226",
"33226",
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"42965",
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"49205",
"53954",
"57125",
"58913",
"66193",
"71674",
"79682",
"85685",
"94421",
"100946",
"110410",
"113290",
"115202"
]
| [
"nonn"
]
| 11 | 1 | 1 | [
"A031396",
"A130227",
"A182468",
"A356488"
]
| null | Jinyuan Wang, Aug 09 2022 | 2022-08-11T14:49:21 | oeisdata/seq/A356/A356488.seq | 136e237dc79ce5557fd258eb958cdd68 |
A356489 | a(n) = A000265(rad(prime(n)-1)), rad = A007947. | [
"1",
"1",
"1",
"3",
"5",
"3",
"1",
"3",
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"39",
"79",
"165",
"21",
"173",
"87",
"11",
"179"
]
| [
"nonn",
"easy"
]
| 11 | 1 | 4 | [
"A000265",
"A007947",
"A057023",
"A077063",
"A204455",
"A356489"
]
| null | Jianing Song, Aug 09 2022 | 2022-08-09T10:56:35 | oeisdata/seq/A356/A356489.seq | b235db69e6e8cf8c89574f177dd85ce9 |
A356490 | a(n) is the determinant of a symmetric Toeplitz matrix M(n) whose first row consists of prime(1), prime(2), ..., prime(n). | [
"1",
"2",
"-5",
"12",
"-19",
"-22",
"1143",
"-4284",
"14265",
"-46726",
"-84405",
"1306096",
"32312445",
"522174906",
"4105967871",
"5135940112",
"-642055973735",
"-2832632334858",
"14310549077571",
"380891148658140",
"4888186898996125",
"-49513565563840210",
"383405170118692791",
"-2517836083641473036",
"-3043377347606882055"
]
| [
"sign"
]
| 25 | 0 | 2 | [
"A005843",
"A309131",
"A350955",
"A350956",
"A356483",
"A356490",
"A356491"
]
| null | Stefano Spezia, Aug 09 2022 | 2023-01-31T05:35:07 | oeisdata/seq/A356/A356490.seq | 21d626d108ae0ca670cba31dd0d71f03 |
A356491 | a(n) is the permanent of a symmetric Toeplitz matrix M(n) whose first row consists of prime(1), prime(2), ..., prime(n). | [
"1",
"2",
"13",
"184",
"4745",
"215442",
"14998965",
"1522204560",
"208682406913",
"37467772675962",
"8809394996942597",
"2597094620811897948",
"954601857873086235553",
"428809643170145564168434",
"229499307540038336275308821",
"144367721963876506217872778284",
"106064861375232790889279725340713"
]
| [
"nonn"
]
| 25 | 0 | 2 | [
"A005843",
"A309131",
"A351021",
"A351022",
"A356483",
"A356490",
"A356491"
]
| null | Stefano Spezia, Aug 09 2022 | 2023-01-31T05:36:23 | oeisdata/seq/A356/A356491.seq | 4c282ab4554ad2ec650d849f693722d3 |
A356492 | a(n) is the determinant of a symmetric Toeplitz matrix M(n) whose first row consists of prime(n), prime(n-1), ..., prime(1). | [
"1",
"2",
"5",
"51",
"264",
"19532",
"-11904",
"1261296",
"-2052864",
"70621632",
"24618221568",
"3996020736",
"743171562496",
"24567175118848",
"-1257930752000",
"864893030400",
"12289833785344000",
"1099483729459478528",
"100515455071223808",
"757166323365314560",
"6294658173770137600",
"7801939905505132544"
]
| [
"sign"
]
| 20 | 0 | 2 | [
"A033286",
"A350955",
"A350956",
"A356484",
"A356492",
"A356493"
]
| null | Stefano Spezia, Aug 09 2022 | 2023-10-13T12:28:14 | oeisdata/seq/A356/A356492.seq | 49150eadf051da318fe20a291855b861 |
A356493 | a(n) is the permanent of a symmetric Toeplitz matrix M(n) whose first row consists of prime(n), prime(n-1), ..., prime(1). | [
"1",
"2",
"13",
"271",
"12030",
"1346758",
"214022024",
"51763672608",
"16088934953136",
"6611717516842608",
"4412314619046451200",
"3533754988232088933120",
"3506189715435673999194112",
"4444138735439968822425464576",
"5893766827264238066914528545792",
"8502284313901016361834901076874240",
"15350799440394462109333953415858960384"
]
| [
"nonn"
]
| 16 | 0 | 2 | [
"A033286",
"A351021",
"A351022",
"A356484",
"A356492",
"A356493"
]
| null | Stefano Spezia, Aug 09 2022 | 2023-10-13T11:50:34 | oeisdata/seq/A356/A356493.seq | 7e20b54415510721c06968b7a5be351b |
A356494 | Expansion of e.g.f. Product_{k>0} B(k * x^k) where B(x) = exp(exp(x)-1) = e.g.f. of Bell numbers. | [
"1",
"1",
"6",
"35",
"327",
"2892",
"37943",
"459895",
"7330172",
"116054835",
"2168292295",
"41072348550",
"898738816957",
"19782331776937",
"487091519709590",
"12305361661242275",
"337777113607935587",
"9528258228302443724",
"289373132780801591323",
"9016757353084706862647"
]
| [
"nonn"
]
| 11 | 0 | 3 | [
"A000110",
"A209903",
"A346055",
"A354843",
"A356460",
"A356494",
"A356495"
]
| null | Seiichi Manyama, Aug 09 2022 | 2022-08-09T11:20:15 | oeisdata/seq/A356/A356494.seq | 24c20c6667e6ef698f6d6e4370bbc272 |
A356495 | Expansion of e.g.f. Product_{k>0} B((k * x)^k) where B(x) = exp(exp(x)-1) = e.g.f. of Bell numbers. | [
"1",
"1",
"10",
"191",
"7287",
"424292",
"37434683",
"4512452023",
"726390985036",
"149098938941283",
"38187088904721655",
"11903871288193251930",
"4442392007373264794677",
"1953788894138983864638457",
"1000334575509506861927067378",
"589712001176601700420819946615"
]
| [
"nonn"
]
| 8 | 0 | 3 | [
"A000110",
"A209903",
"A346055",
"A354892",
"A356494",
"A356495"
]
| null | Seiichi Manyama, Aug 09 2022 | 2022-08-09T11:20:47 | oeisdata/seq/A356/A356495.seq | fc4665a726b990486c4491544681478c |
A356496 | Squarefree integers k such that x^4 - k*y^2 = 1 has a nontrivial solution. | [
"5",
"6",
"15",
"29",
"39",
"145",
"210",
"255",
"410",
"455",
"791",
"905",
"915",
"985",
"1111",
"1295",
"1785",
"2031",
"3603",
"3815",
"4199",
"7215",
"8547",
"8555",
"10421",
"12155",
"13015",
"13271",
"14430",
"16913",
"17490",
"18530",
"20735",
"22327",
"24414",
"26390",
"28230",
"29039",
"33215",
"36411",
"38415",
"41943",
"44205",
"54795",
"60639",
"61535",
"63546"
]
| [
"nonn"
]
| 8 | 1 | 1 | null | null | Michel Marcus, Aug 09 2022 | 2022-08-09T14:11:30 | oeisdata/seq/A356/A356496.seq | 4328f511056b329209e290966f3f64e9 |
A356497 | a(n) = maximal 2^k such that there exists a (2^k)-th root of unity modulo n. | [
"1",
"1",
"2",
"2",
"4",
"2",
"2",
"2",
"2",
"4",
"2",
"2",
"4",
"2",
"4",
"4",
"16",
"2",
"2",
"4",
"2",
"2",
"2",
"2",
"4",
"4",
"2",
"2",
"4",
"4",
"2",
"8",
"2",
"16",
"4",
"2",
"4",
"2",
"4",
"4",
"8",
"2",
"2",
"2",
"4",
"2",
"2",
"4",
"2",
"4",
"16",
"4",
"4",
"2",
"4",
"2",
"2",
"4",
"2",
"4",
"4",
"2",
"2",
"16",
"4",
"2",
"2",
"16",
"2",
"4",
"2",
"2",
"8",
"4",
"4",
"2",
"2",
"4",
"2",
"4",
"2",
"8",
"2",
"2",
"16",
"2",
"4",
"2",
"8",
"4",
"4",
"2",
"2",
"2",
"4",
"8",
"32",
"2",
"2",
"4"
]
| [
"nonn"
]
| 8 | 1 | 3 | null | null | Dmitry Grekov, Aug 09 2022 | 2022-10-02T00:55:50 | oeisdata/seq/A356/A356497.seq | e7e035e989de820f03860ccb4431a77c |
A356498 | Primes p such that 100*p + 11 is also prime. | [
"2",
"3",
"23",
"41",
"83",
"101",
"107",
"113",
"137",
"179",
"233",
"239",
"251",
"281",
"293",
"353",
"359",
"401",
"419",
"479",
"503",
"557",
"563",
"569",
"587",
"683",
"701",
"743",
"809",
"839",
"857",
"863",
"941",
"953",
"977",
"1049",
"1091",
"1103",
"1193",
"1217",
"1277",
"1283",
"1361",
"1367",
"1427",
"1487",
"1499",
"1523",
"1607",
"1619",
"1847",
"1871",
"1877",
"1889",
"1907",
"1949",
"1973"
]
| [
"nonn"
]
| 17 | 1 | 1 | [
"A000040",
"A002476",
"A023237",
"A356498"
]
| null | Daniel Blam, Aug 09 2022 | 2022-09-11T16:50:44 | oeisdata/seq/A356/A356498.seq | 14b42693a8011998cf828686217d1dfc |
A356499 | G.f. A(x) satisfies: x = Product_{n>=1} (1 - x^n*A(x)) * (1 - x^(n-1)/A(x)). | [
"1",
"1",
"3",
"10",
"32",
"108",
"382",
"1419",
"5437",
"21288",
"84618",
"340499",
"1384711",
"5683834",
"23520471",
"98018975",
"410998473",
"1732666697",
"7339612244",
"31224662178",
"133353750962",
"571527895700",
"2457293364403",
"10596053295516",
"45813536708704",
"198570001079591",
"862624530201300"
]
| [
"nonn"
]
| 15 | 0 | 3 | [
"A000041",
"A356499",
"A356508"
]
| null | Paul D. Hanna, Aug 11 2022 | 2023-10-04T04:19:26 | oeisdata/seq/A356/A356499.seq | 2c601824b72929aec3fd51f96c3c7f46 |
A356500 | Coefficients T(n,k) of x^n*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. | [
"0",
"1",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"4",
"0",
"0",
"0",
"4",
"0",
"0",
"6",
"0",
"0",
"0",
"28",
"0",
"0",
"0",
"22",
"0",
"3",
"0",
"0",
"0",
"84",
"0",
"0",
"0",
"219",
"0",
"0",
"0",
"140",
"0",
"0",
"0",
"0",
"135",
"0",
"0",
"0",
"981",
"0",
"0",
"0",
"1807",
"0",
"0",
"0",
"969",
"0",
"0",
"0",
"120",
"0",
"0",
"0",
"2568",
"0",
"0",
"0",
"10764",
"0",
"0",
"0",
"15368",
"0",
"0",
"0",
"7084",
"0",
"0",
"54",
"0",
"0",
"0",
"4284",
"0",
"0",
"0",
"38896",
"0",
"0",
"0",
"114240",
"0",
"0",
"0",
"133266",
"0",
"0",
"0",
"53820",
"0",
"9",
"0",
"0",
"0",
"4662",
"0",
"0",
"0",
"94390",
"0",
"0",
"0",
"525980",
"0",
"0",
"0",
"1187433",
"0",
"0",
"0",
"1171390",
"0",
"0",
"0",
"420732"
]
| [
"nonn",
"tabf"
]
| 24 | 0 | 11 | [
"A000716",
"A002293",
"A354248",
"A354655",
"A354656",
"A355350",
"A355360",
"A355365",
"A355870",
"A355872",
"A356500",
"A356501",
"A356502",
"A356503",
"A356504",
"A356505"
]
| null | Paul D. Hanna, Aug 09 2022 | 2025-03-23T18:38:47 | oeisdata/seq/A356/A356500.seq | 7126696c47490a55a7a387c4245e3dc3 |
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