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2.35k
| offset_a
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666,262,453B
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635M
⌀ | cross_references
listlengths 1
128
⌀ | former_ids
listlengths 1
3
⌀ | author
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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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|---|---|---|---|---|---|---|---|---|---|---|---|---|
A363501 | a(n) = smallest product > n of some subset of the divisors of n, or if no product > n exists then a(n) = n. | [
"1",
"2",
"3",
"8",
"5",
"12",
"7",
"16",
"27",
"20",
"11",
"18",
"13",
"28",
"45",
"32",
"17",
"27",
"19",
"40",
"63",
"44",
"23",
"32",
"125",
"52",
"81",
"56",
"29",
"36",
"31",
"64",
"99",
"68",
"175",
"48",
"37",
"76",
"117",
"50",
"41",
"63",
"43",
"88",
"75",
"92",
"47",
"64",
"343",
"100",
"153",
"104",
"53",
"81",
"275",
"64",
"171",
"116",
"59",
"72",
"61",
"124",
"147"
]
| [
"nonn"
]
| 28 | 1 | 2 | [
"A027750",
"A363501",
"A363627"
]
| null | Denis Ivanov, Jun 06 2023 | 2023-06-17T14:22:44 | oeisdata/seq/A363/A363501.seq | 6135efada0a91314afb326afb8b538d8 |
A363502 | Decimal expansion of Product_{k>=1} k*sinh(1/k). | [
"1",
"3",
"0",
"7",
"9",
"7",
"0",
"9",
"3",
"6",
"6",
"6",
"4",
"2",
"8",
"3",
"6",
"4",
"9",
"0",
"1",
"2",
"1",
"0",
"4",
"4",
"7",
"6",
"0",
"0",
"7",
"0",
"5",
"6",
"3",
"2",
"0",
"4",
"6",
"5",
"5",
"1",
"5",
"6",
"8",
"3",
"1",
"3",
"8",
"2",
"2",
"3",
"5",
"0",
"6",
"7",
"0",
"5",
"6",
"4",
"8",
"2",
"2",
"5",
"9",
"7",
"9",
"2",
"2",
"9",
"3",
"0",
"9",
"8",
"0",
"0",
"9",
"9",
"5",
"4",
"3",
"6",
"4",
"3",
"2",
"1",
"9",
"2",
"2",
"8",
"4",
"8",
"3",
"5",
"9",
"9",
"9",
"0",
"4",
"7",
"0",
"1",
"3",
"7",
"6"
]
| [
"nonn",
"cons"
]
| 21 | 1 | 2 | [
"A027641",
"A027642",
"A118817",
"A249673",
"A295219",
"A363502"
]
| null | Amiram Eldar, Jul 30 2023 | 2023-07-30T02:26:40 | oeisdata/seq/A363/A363502.seq | 522eb912809c46f10f781d743c9e0942 |
A363503 | a(n+1) = 2*a(n) + A298338(n-1), with a(1) = 1. | [
"1",
"3",
"7",
"15",
"33",
"71",
"151",
"319",
"667",
"1385",
"2855",
"5855",
"11949",
"24299",
"49255",
"99597",
"200967",
"404845",
"814425",
"1636581",
"3285713",
"6591853",
"13216829",
"26487447",
"53062045",
"106265431",
"212759755",
"425890401",
"852381243",
"1705734905",
"3413043757",
"6828635653",
"13661395165"
]
| [
"nonn"
]
| 64 | 1 | 2 | [
"A104457",
"A298338",
"A363503"
]
| null | Evangelos G. Filothodoros, Jun 06 2023 | 2023-08-02T07:10:30 | oeisdata/seq/A363/A363503.seq | 483498eccf870ed6e6dd727ccc803a7b |
A363504 | a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared that is a multiple of prime(Omega(a(n-1))). | [
"1",
"2",
"4",
"3",
"6",
"9",
"12",
"5",
"8",
"10",
"15",
"18",
"20",
"25",
"21",
"24",
"7",
"14",
"27",
"30",
"35",
"33",
"36",
"28",
"40",
"42",
"45",
"50",
"55",
"39",
"48",
"11",
"16",
"49",
"51",
"54",
"56",
"63",
"60",
"70",
"65",
"57",
"66",
"75",
"80",
"22",
"69",
"72",
"44",
"85",
"78",
"90",
"77",
"81",
"84",
"91",
"87",
"93",
"96",
"13",
"26",
"99",
"95",
"102",
"100",
"98",
"105",
"110",
"115",
"108",
"88",
"112",
"121",
"111"
]
| [
"nonn"
]
| 17 | 1 | 2 | [
"A000040",
"A001222",
"A351495",
"A363504",
"A363956"
]
| null | Scott R. Shannon, Jun 06 2023 | 2023-07-02T09:17:27 | oeisdata/seq/A363/A363504.seq | 07bae31e7050b2c9cfa9c1cf36902db6 |
A363505 | Number of hyperplanes spanned by the vertices of an n-cube up to symmetry. | [
"2",
"3",
"6",
"15",
"63",
"623",
"22432",
"3899720"
]
| [
"nonn",
"hard",
"more"
]
| 20 | 2 | 1 | [
"A007847",
"A363505",
"A363506",
"A363512"
]
| null | Jörg Rambau, Jun 06 2023 | 2023-06-08T10:57:42 | oeisdata/seq/A363/A363505.seq | d81d167985b1b60917a81302237a709a |
A363506 | The number of affine dependencies among the vertices of the n-cube up to symmetry. | [
"1",
"3",
"15",
"186",
"12628",
"3591868",
"3858105362"
]
| [
"nonn",
"hard",
"more"
]
| 13 | 2 | 2 | [
"A007847",
"A363505",
"A363506",
"A363512"
]
| null | Jörg Rambau, Jun 06 2023 | 2023-06-08T10:57:38 | oeisdata/seq/A363/A363506.seq | 5cb6460c1653fc5a0acc613a58c45efc |
A363507 | G.f. satisfies A(x) = exp( Sum_{k>=1} (3 + A(x^k)) * x^k/k ). | [
"1",
"4",
"14",
"50",
"191",
"763",
"3180",
"13640",
"59937",
"268304",
"1219626",
"5614038",
"26117296",
"122598622",
"579977691",
"2762264225",
"13234003724",
"63737225733",
"308406648979",
"1498558628584",
"7309116199687",
"35772044402485",
"175621484712091",
"864670723348447"
]
| [
"nonn"
]
| 14 | 0 | 2 | [
"A000081",
"A029857",
"A036249",
"A363507",
"A363508",
"A363509"
]
| null | Seiichi Manyama, Jun 06 2023 | 2023-06-07T09:45:14 | oeisdata/seq/A363/A363507.seq | c7aa8166553f38b195199fe178ef7456 |
A363508 | G.f. satisfies A(x) = exp( Sum_{k>=1} (4 + A(x^k)) * x^k/k ). | [
"1",
"5",
"20",
"80",
"340",
"1516",
"7046",
"33736",
"165436",
"826566",
"4193348",
"21542664",
"111848161",
"585949358",
"3093526496",
"16442687695",
"87914559018",
"472522551440",
"2551591234444",
"13836226412386",
"75311992329508",
"411336641019998",
"2253641429297336"
]
| [
"nonn"
]
| 14 | 0 | 2 | [
"A000081",
"A029857",
"A036249",
"A363507",
"A363508",
"A363510"
]
| null | Seiichi Manyama, Jun 06 2023 | 2023-06-07T00:08:14 | oeisdata/seq/A363/A363508.seq | cec255fa6b8d9531814a30aaa3661da7 |
A363509 | G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * (3 + A(x^k)) * x^k/k ). | [
"1",
"4",
"10",
"30",
"101",
"361",
"1354",
"5238",
"20740",
"83683",
"342719",
"1421019",
"5953306",
"25162342",
"107163924",
"459438524",
"1981247950",
"8588054014",
"37398421941",
"163534601567",
"717776072291",
"3161117717887",
"13964782042188",
"61866495037806",
"274792382789958"
]
| [
"nonn"
]
| 15 | 0 | 2 | [
"A004111",
"A038075",
"A038076",
"A363507",
"A363509",
"A363510"
]
| null | Seiichi Manyama, Jun 06 2023 | 2025-05-10T15:19:13 | oeisdata/seq/A363/A363509.seq | 12c4a15a9fd34a832e0fd083fc8ba1fd |
A363510 | G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * (4 + A(x^k)) * x^k/k ). | [
"1",
"5",
"15",
"50",
"190",
"766",
"3231",
"14066",
"62681",
"284591",
"1311622",
"6120183",
"28855529",
"137257541",
"657894518",
"3174411715",
"15406640415",
"75162477018",
"368383443235",
"1813007892858",
"8956214966017",
"44393932344984",
"220732441125743",
"1100621484436502"
]
| [
"nonn"
]
| 14 | 0 | 2 | [
"A004111",
"A038075",
"A038076",
"A363508",
"A363509",
"A363510"
]
| null | Seiichi Manyama, Jun 06 2023 | 2023-06-07T09:45:05 | oeisdata/seq/A363/A363510.seq | 4383b704465c047703ef036488f5b861 |
A363511 | Number of partitions of [n] having exactly one parity change within their blocks. | [
"0",
"0",
"1",
"2",
"6",
"18",
"61",
"210",
"778",
"3008",
"12219",
"52268",
"231726",
"1083012",
"5202199",
"26307710",
"135972580",
"738339310",
"4081523615",
"23649300862",
"139096468520",
"855529383396",
"5329630673249",
"34643027568520",
"227682351175868",
"1558106351450416",
"10766192988109009"
]
| [
"nonn"
]
| 10 | 0 | 4 | [
"A000110",
"A124419",
"A363493",
"A363511"
]
| null | Alois P. Heinz, Jun 06 2023 | 2023-06-06T20:00:20 | oeisdata/seq/A363/A363511.seq | cdfcfe394b6d295d5f596a7623f9ecdc |
A363512 | The number of affine dependencies among the vertices of the n-cube. | [
"1",
"20",
"1348",
"353616",
"446148992",
"2118502178496",
"38636185528212416"
]
| [
"nonn",
"hard",
"more"
]
| 25 | 2 | 2 | [
"A007847",
"A363505",
"A363506",
"A363512"
]
| null | Jörg Rambau, Jun 08 2023 | 2023-06-12T01:10:14 | oeisdata/seq/A363/A363512.seq | 73d8109adf8ab59f3830085605eb9f9a |
A363513 | a(1) = 2, then a(n) is the least prime p > a(n - 1) such that p + a(n-1) and p - a(n-1) have the same number of prime factors counted with multiplicity. | [
"2",
"5",
"13",
"31",
"61",
"103",
"157",
"173",
"181",
"193",
"211",
"223",
"239",
"269",
"313",
"337",
"353",
"419",
"487",
"499",
"577",
"613",
"631",
"647",
"677",
"709",
"727",
"827",
"857",
"947",
"1039",
"1093",
"1117",
"1231",
"1283",
"1303",
"1319",
"1483",
"1499",
"1553",
"1609",
"1627",
"1657",
"1693",
"1721",
"1733",
"1823",
"1913",
"1933",
"1951",
"2003",
"2027",
"2039",
"2129",
"2161",
"2203"
]
| [
"nonn"
]
| 26 | 1 | 1 | [
"A001222",
"A361611",
"A363513"
]
| null | Zak Seidov and Robert Israel, Jun 07 2023 | 2023-06-11T14:18:55 | oeisdata/seq/A363/A363513.seq | 62649f32b02cd9159be51e810a4d0e86 |
A363514 | Sum of divisors of 3*n-1 of form 3*k+1. | [
"1",
"1",
"5",
"1",
"8",
"1",
"15",
"1",
"14",
"1",
"21",
"8",
"20",
"1",
"27",
"1",
"36",
"1",
"40",
"1",
"32",
"14",
"39",
"1",
"38",
"8",
"71",
"1",
"44",
"1",
"51",
"20",
"57",
"1",
"70",
"1",
"88",
"1",
"63",
"8",
"62",
"26",
"85",
"1",
"68",
"1",
"120",
"14",
"74",
"1",
"100",
"32",
"80",
"8",
"87",
"1",
"130",
"1",
"131",
"1",
"112",
"38",
"99",
"1",
"98",
"1",
"180",
"8",
"104",
"20",
"111",
"44",
"110",
"14",
"168",
"1",
"172",
"1"
]
| [
"nonn"
]
| 52 | 1 | 3 | [
"A078181",
"A359211",
"A363514",
"A363889",
"A363890",
"A363891"
]
| null | Seiichi Manyama, Jun 26 2023 | 2023-06-27T09:17:11 | oeisdata/seq/A363/A363514.seq | 47eea999663089b698f746cbce98fbfb |
A363515 | Numerator of log(2) + (-1/4)^n*Integral_{x=0..1} (1 - x)^(4*n+2)/(1 + x^2) dx. | [
"1",
"79",
"14087",
"3990557",
"217474889",
"10326377909",
"19001942777579",
"3306285643032971",
"3279846716611480357",
"121354235196693865579",
"19902098013482397470501",
"1711580361934007500382731",
"9009759106282339175994464009",
"59689653955233943488755746919",
"3820137854975012405338172218301"
]
| [
"nonn",
"frac",
"less"
]
| 25 | 0 | 2 | [
"A002162",
"A004767",
"A016825",
"A262710",
"A363515",
"A363516"
]
| null | Alexander R. Povolotsky and Stefano Spezia, Jun 07 2023 | 2023-08-02T14:01:10 | oeisdata/seq/A363/A363515.seq | 2e92f695c91a43d09eef8ec4f188b2cd |
A363516 | Denominator of log(2) + (-1/4)^n*Integral_{x=0..1} (1 - x)^(4*n+2)/(1 + x^2) dx. | [
"1",
"120",
"20160",
"5765760",
"313657344",
"14898723840",
"27413651865600",
"4769975424614400",
"4731815621217484800",
"175077177985046937600",
"28712657189547697766400",
"2469288518301102007910400",
"12998334760337000969640345600",
"86113967787232631423867289600",
"5511293938382888411127506534400"
]
| [
"nonn",
"frac"
]
| 20 | 0 | 2 | [
"A002162",
"A004767",
"A016825",
"A262710",
"A363515",
"A363516"
]
| null | Alexander R. Povolotsky and Stefano Spezia, Jun 07 2023 | 2023-08-02T14:01:29 | oeisdata/seq/A363/A363516.seq | bdcd8c5e422aefe2d64f210ff994680e |
A363517 | Number of ways to choose 4 disjoint subsets of {1..n} with the same sum and with respectively 1, 2, 3 and 4 distinct elements of {1..n}. | [
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"6",
"18",
"57",
"155",
"351",
"714",
"1386",
"2495",
"4291",
"7043",
"11234",
"17270",
"26087",
"38105",
"54954",
"77453",
"107816",
"146881",
"198880",
"264222",
"348722",
"453447",
"586339",
"747970",
"950770",
"1193145",
"1492469",
"1848124",
"2280697",
"2787353",
"3400200",
"4110662",
"4959054",
"5937538"
]
| [
"nonn",
"nice"
]
| 43 | 0 | 16 | [
"A362717",
"A363517"
]
| null | Jean-Marc Rebert, Jun 07 2023 | 2023-09-06T21:20:10 | oeisdata/seq/A363/A363517.seq | f71f9b626afa82de320ab4822b9d003d |
A363518 | Concentric square numbers on the faces of an n X n X n cube. | [
"1",
"8",
"20",
"32",
"50",
"80",
"116",
"152",
"194",
"248",
"308",
"368",
"434",
"512",
"596",
"680",
"770",
"872",
"980",
"1088",
"1202",
"1328",
"1460",
"1592",
"1730",
"1880",
"2036",
"2192",
"2354",
"2528",
"2708",
"2888",
"3074",
"3272",
"3476",
"3680",
"3890",
"4112",
"4340",
"4568",
"4802",
"5048",
"5300",
"5552",
"5810",
"6080",
"6356",
"6632",
"6914",
"7208",
"7508",
"7808"
]
| [
"nonn",
"easy"
]
| 15 | 1 | 2 | [
"A194274",
"A363518"
]
| null | Nicolay Avilov, Jun 07 2023 | 2023-07-15T14:26:10 | oeisdata/seq/A363/A363518.seq | 73373c77b46fe1136fc834021ca08883 |
A363519 | Number T(n,k) of partitions of [n] having exactly k parity changes within the partition, n>=0, 0<=k<=max(0,n-1), read by rows. | [
"1",
"1",
"0",
"2",
"0",
"1",
"4",
"0",
"3",
"4",
"8",
"0",
"2",
"18",
"14",
"18",
"0",
"7",
"27",
"87",
"42",
"40",
"0",
"5",
"102",
"162",
"360",
"147",
"101",
"0",
"20",
"179",
"866",
"931",
"1456",
"434",
"254",
"0",
"15",
"675",
"1746",
"5836",
"4755",
"5778",
"1619",
"723",
"0",
"67",
"1321",
"9087",
"16416",
"36031",
"22893",
"23052",
"5044",
"2064",
"0",
"52",
"5216",
"19863",
"93452",
"117172",
"206570",
"115178",
"94210",
"20271",
"6586"
]
| [
"nonn",
"tabf"
]
| 28 | 0 | 4 | [
"A000110",
"A274547",
"A363493",
"A363519",
"A363549",
"A363550"
]
| null | Alois P. Heinz, Jun 07 2023 | 2023-11-17T11:21:10 | oeisdata/seq/A363/A363519.seq | 619b888e0428d421f1e3a270618ef16c |
A363520 | Product of the divisors of n that are < sqrt(n). | [
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"6",
"1",
"2",
"3",
"2",
"1",
"6",
"1",
"8",
"3",
"2",
"1",
"24",
"1",
"2",
"3",
"8",
"1",
"30",
"1",
"8",
"3",
"2",
"5",
"24",
"1",
"2",
"3",
"40",
"1",
"36",
"1",
"8",
"15",
"2",
"1",
"144",
"1",
"10",
"3",
"8",
"1",
"36",
"5",
"56",
"3",
"2",
"1",
"720",
"1",
"2",
"21",
"8",
"5",
"36",
"1",
"8",
"3",
"70",
"1",
"1152",
"1",
"2",
"15",
"8",
"7",
"36",
"1",
"320",
"3",
"2",
"1"
]
| [
"nonn",
"easy"
]
| 20 | 1 | 6 | [
"A000196",
"A010052",
"A070039",
"A072499",
"A363520",
"A363521"
]
| null | Wesley Ivan Hurt, Jun 07 2023 | 2023-06-17T11:21:35 | oeisdata/seq/A363/A363520.seq | d516e043ad36fae13debc1591df1e879 |
A363521 | Product of the divisors d of n such that sqrt(n) < d < n. | [
"1",
"1",
"1",
"1",
"1",
"3",
"1",
"4",
"1",
"5",
"1",
"24",
"1",
"7",
"5",
"8",
"1",
"54",
"1",
"50",
"7",
"11",
"1",
"576",
"1",
"13",
"9",
"98",
"1",
"900",
"1",
"128",
"11",
"17",
"7",
"1944",
"1",
"19",
"13",
"1600",
"1",
"2058",
"1",
"242",
"135",
"23",
"1",
"36864",
"1",
"250",
"17",
"338",
"1",
"4374",
"11",
"3136",
"19",
"29",
"1",
"1080000",
"1",
"31",
"189",
"512",
"13",
"7986",
"1",
"578",
"23"
]
| [
"nonn",
"easy"
]
| 12 | 1 | 6 | [
"A007955",
"A007956",
"A072499",
"A363520",
"A363521"
]
| null | Wesley Ivan Hurt, Jun 07 2023 | 2023-06-17T11:25:31 | oeisdata/seq/A363/A363521.seq | 278dd8273596e53d8d35636e1de1b11c |
A363522 | Number of integers k such that there are exactly n distinct numbers j with k^2 < j < (k+1)^2 which can be expressed as sum of two squares. | [
"1",
"1",
"2",
"1",
"2",
"1",
"3",
"1",
"2",
"1",
"2",
"3",
"2",
"1",
"1",
"3",
"2",
"2",
"1",
"3",
"3",
"1",
"3",
"1",
"2",
"1",
"4",
"2",
"1",
"3",
"1",
"3",
"1",
"3",
"1",
"4",
"1",
"3",
"2",
"1",
"1",
"4",
"1",
"4",
"2",
"3",
"0",
"2",
"3",
"3",
"3",
"2",
"2",
"2",
"1",
"0",
"3",
"5",
"1",
"4",
"1",
"4",
"0",
"2",
"2",
"3",
"4",
"1",
"1",
"3",
"3",
"0",
"5",
"1",
"4",
"1",
"2",
"1",
"3",
"4",
"0",
"3",
"3",
"2",
"2",
"4",
"0",
"3"
]
| [
"nonn"
]
| 36 | 0 | 3 | [
"A077773",
"A363522",
"A363761",
"A363762",
"A363763"
]
| null | Rainer Rosenthal, Jul 07 2023 | 2023-07-10T12:13:24 | oeisdata/seq/A363/A363522.seq | 0953f9d356896ad203d441de6b1ada14 |
A363523 | k is a term of this sequence if and only if Clausen(k, 0) divides Clausen(k, 2). (Clausen = A160014.) | [
"1",
"3",
"9",
"15",
"27",
"45",
"75",
"81",
"99",
"105",
"135",
"225",
"243",
"255",
"297",
"315",
"375",
"405",
"495",
"525",
"675",
"729",
"735",
"765",
"783",
"891",
"945",
"1089",
"1125",
"1215",
"1275",
"1287",
"1485",
"1575",
"1785",
"1875",
"2025",
"2115",
"2187",
"2205",
"2295",
"2349",
"2415",
"2475",
"2625",
"2673",
"2835",
"3267",
"3375",
"3465"
]
| [
"nonn"
]
| 9 | 1 | 2 | [
"A124240",
"A160014",
"A363523"
]
| null | Peter Luschny, Jun 08 2023 | 2023-06-08T08:49:30 | oeisdata/seq/A363/A363523.seq | 8194e83be3b2335a01bd509ddb9e837a |
A363524 | a(n) = 0 if 4 divides n + 1, otherwise (-1)^floor((n + 1) / 4) * 2^floor(n / 2). | [
"1",
"1",
"2",
"0",
"-4",
"-4",
"-8",
"0",
"16",
"16",
"32",
"0",
"-64",
"-64",
"-128",
"0",
"256",
"256",
"512",
"0",
"-1024",
"-1024",
"-2048",
"0",
"4096",
"4096",
"8192",
"0",
"-16384",
"-16384",
"-32768",
"0",
"65536",
"65536",
"131072",
"0",
"-262144",
"-262144",
"-524288",
"0",
"1048576",
"1048576",
"2097152",
"0",
"-4194304",
"-4194304"
]
| [
"sign",
"easy"
]
| 23 | 0 | 3 | [
"A016116",
"A046978",
"A153641",
"A363524"
]
| null | Peter Luschny, Jun 17 2023 | 2023-08-06T08:16:33 | oeisdata/seq/A363/A363524.seq | c4d25bfc8d924c023f679bf670600069 |
A363525 | Number of integer partitions of n with weighted sum divisible by reverse-weighted sum. | [
"1",
"2",
"2",
"3",
"2",
"4",
"2",
"4",
"5",
"5",
"3",
"10",
"4",
"7",
"13",
"10",
"8",
"29",
"10",
"18",
"39",
"20",
"20",
"70",
"29",
"40",
"105",
"65",
"55",
"166",
"73",
"132",
"242",
"141",
"129",
"476",
"183",
"248",
"580",
"487",
"312",
"984",
"422",
"868",
"1345",
"825",
"724",
"2709",
"949",
"1505",
"2756",
"2902",
"1611",
"4664",
"2289",
"4942",
"5828",
"4278"
]
| [
"nonn"
]
| 9 | 1 | 2 | [
"A000005",
"A000009",
"A000016",
"A000041",
"A008284",
"A029931",
"A053632",
"A067538",
"A222855",
"A222970",
"A264034",
"A304818",
"A318283",
"A320387",
"A358136",
"A358137",
"A358194",
"A359042",
"A359361",
"A359678",
"A359755",
"A362558",
"A362559",
"A362560",
"A363525",
"A363526",
"A363527",
"A363528",
"A363530",
"A363531"
]
| null | Gus Wiseman, Jun 10 2023 | 2023-06-11T11:18:36 | oeisdata/seq/A363/A363525.seq | c8a3a24ec09944091dc578ba94195f57 |
A363526 | Number of integer partitions of n with reverse-weighted sum 3*n. | [
"1",
"0",
"0",
"0",
"0",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"2",
"2",
"2",
"4",
"3",
"2",
"4",
"4",
"4",
"5",
"5",
"4",
"7",
"7",
"5",
"8",
"7",
"6",
"11",
"9",
"8",
"11",
"10",
"10",
"13",
"12",
"11",
"15",
"15",
"12",
"17",
"16",
"14",
"20",
"18",
"16",
"22",
"20",
"19",
"24",
"22",
"20",
"27",
"26",
"23",
"29",
"27",
"25",
"33",
"30",
"28",
"35",
"33",
"31",
"38",
"36",
"33",
"41",
"40"
]
| [
"nonn"
]
| 10 | 0 | 11 | [
"A000009",
"A000016",
"A000041",
"A008284",
"A029931",
"A053632",
"A067538",
"A079998",
"A222855",
"A222970",
"A231429",
"A264034",
"A304818",
"A318283",
"A320387",
"A358136",
"A358194",
"A359042",
"A359361",
"A359678",
"A359755",
"A360672",
"A360675",
"A362559",
"A362560",
"A363525",
"A363526",
"A363527",
"A363528",
"A363530",
"A363531"
]
| null | Gus Wiseman, Jun 10 2023 | 2023-06-12T08:44:13 | oeisdata/seq/A363/A363526.seq | e1a10c1cea6bc604d786b3f30ec0956c |
A363527 | Number of integer partitions of n with weighted sum 3*n. | [
"1",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"1",
"1",
"1",
"1",
"1",
"1",
"3",
"4",
"4",
"6",
"8",
"7",
"10",
"13",
"13",
"21",
"25",
"24",
"37",
"39",
"40",
"58",
"63",
"72",
"94",
"106",
"118",
"144",
"165",
"181",
"224",
"256",
"277",
"341",
"387",
"417",
"504",
"560",
"615",
"743",
"818",
"899",
"1066",
"1171",
"1285",
"1502",
"1655",
"1819",
"2108",
"2315",
"2547",
"2915"
]
| [
"nonn"
]
| 7 | 0 | 15 | [
"A000009",
"A000016",
"A000041",
"A008284",
"A029931",
"A053632",
"A067538",
"A222855",
"A222970",
"A231429",
"A264034",
"A304818",
"A318283",
"A320387",
"A358136",
"A358194",
"A359042",
"A359361",
"A359678",
"A359755",
"A360672",
"A360675",
"A362559",
"A362560",
"A363525",
"A363526",
"A363527",
"A363528",
"A363531",
"A363532"
]
| null | Gus Wiseman, Jun 11 2023 | 2023-06-19T22:35:35 | oeisdata/seq/A363/A363527.seq | 5a687b2c64917647ed4bfbeea25719a2 |
A363528 | Number of strict integer partitions of n with weighted sum divisible by reverse-weighted sum. | [
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"3",
"1",
"1",
"3",
"1",
"2",
"6",
"2",
"3",
"9",
"3",
"4",
"11",
"4",
"5",
"16",
"6",
"8",
"24",
"8",
"10",
"31",
"11",
"14",
"41",
"18",
"18",
"59",
"21",
"27",
"74",
"30",
"32",
"100",
"35",
"43",
"128",
"54",
"53",
"173",
"58",
"78",
"215",
"81",
"88",
"294",
"97",
"123",
"362",
"150",
"146",
"469",
"162",
"221",
"577"
]
| [
"nonn"
]
| 8 | 1 | 12 | [
"A000009",
"A000041",
"A008284",
"A053632",
"A067538",
"A222855",
"A222970",
"A264034",
"A304818",
"A318283",
"A320387",
"A358136",
"A358137",
"A358194",
"A359361",
"A359678",
"A359754",
"A359755",
"A362558",
"A362559",
"A362560",
"A363525",
"A363526",
"A363528",
"A363531"
]
| null | Gus Wiseman, Jun 10 2023 | 2023-06-11T11:18:31 | oeisdata/seq/A363/A363528.seq | 75173bc63387a6ebc15f65e145b9d5c8 |
A363529 | E.g.f. satisfies A(x) = exp(x * (1 + x * A(x)^4)). | [
"1",
"1",
"3",
"31",
"409",
"7361",
"170251",
"4732351",
"154694961",
"5814634753",
"246946119571",
"11698927124831",
"611660759515081",
"34984757221103041",
"2173041881789331099",
"145669007565799127551",
"10482025117382045382241",
"805892200757926620144641"
]
| [
"nonn"
]
| 12 | 0 | 3 | [
"A125500",
"A143768",
"A363354",
"A363529"
]
| null | Seiichi Manyama, Aug 17 2023 | 2025-02-16T08:34:05 | oeisdata/seq/A363/A363529.seq | 41d34ab1efbee8dadbaa6d446004c67b |
A363530 | Heinz numbers of integer partitions such that 3*(sum) = (weighted sum). | [
"1",
"32",
"40",
"60",
"100",
"126",
"210",
"243",
"294",
"351",
"550",
"585",
"770",
"819",
"1210",
"1274",
"1275",
"1287",
"1521",
"1785",
"2002",
"2366",
"2793",
"2805",
"2875",
"3125",
"3315",
"4025",
"4114",
"4335",
"4389",
"4862",
"5187",
"6325",
"6358",
"6422",
"6783",
"7105",
"7475",
"7581",
"8349",
"8398",
"9386",
"9775",
"9867",
"10925"
]
| [
"nonn"
]
| 7 | 1 | 2 | [
"A000041",
"A000720",
"A001221",
"A001222",
"A046660",
"A053632",
"A055396",
"A056239",
"A061395",
"A106529",
"A112798",
"A118914",
"A124010",
"A181819",
"A215366",
"A264034",
"A304818",
"A318283",
"A320387",
"A358136",
"A358194",
"A359361",
"A359362",
"A359678",
"A359755",
"A363526",
"A363527",
"A363530",
"A363531"
]
| null | Gus Wiseman, Jun 12 2023 | 2023-06-12T08:44:19 | oeisdata/seq/A363/A363530.seq | 0fb6c12362df0a9258697fa2dcaf005a |
A363531 | Heinz numbers of integer partitions such that 3*(sum) = (reverse-weighted sum). | [
"1",
"32",
"144",
"216",
"243",
"672",
"1008",
"1350",
"2176",
"2250",
"2520",
"2673",
"3125",
"3969",
"4160",
"4200",
"5940",
"6240",
"6615",
"7344",
"7424",
"7744",
"8262",
"9261",
"9800",
"9900",
"10400",
"11616",
"12250",
"12312",
"12375",
"13104",
"13720",
"14720",
"14742",
"16767",
"16807",
"17150",
"19360",
"21840",
"22080",
"23100"
]
| [
"nonn"
]
| 5 | 1 | 2 | [
"A000041",
"A000720",
"A001221",
"A001222",
"A046660",
"A053632",
"A055396",
"A056239",
"A061395",
"A106529",
"A112798",
"A118914",
"A124010",
"A181819",
"A215366",
"A264034",
"A304818",
"A318283",
"A320387",
"A358136",
"A358194",
"A359361",
"A359362",
"A359678",
"A359755",
"A363526",
"A363527",
"A363530",
"A363531"
]
| null | Gus Wiseman, Jun 12 2023 | 2023-06-12T08:42:37 | oeisdata/seq/A363/A363531.seq | 83a613bd5657cc55d347641597cc7a11 |
A363532 | Number of integer partitions of n with weighted alternating sum 0. | [
"1",
"0",
"0",
"1",
"0",
"0",
"2",
"2",
"0",
"3",
"3",
"3",
"5",
"5",
"10",
"12",
"7",
"14",
"25",
"18",
"22",
"48",
"48",
"41",
"67",
"82",
"89",
"111",
"140",
"170",
"220",
"214",
"264",
"392",
"386",
"436",
"623",
"693",
"756",
"934",
"1102",
"1301",
"1565",
"1697",
"2132",
"2616",
"2727",
"3192",
"4062",
"4550",
"5000",
"6132",
"7197",
"8067",
"9338",
"10750",
"12683"
]
| [
"nonn"
]
| 6 | 0 | 7 | [
"A000041",
"A008284",
"A035363",
"A053632",
"A106529",
"A261079",
"A264034",
"A304818",
"A316524",
"A318283",
"A320387",
"A344616",
"A358194",
"A360672",
"A360675",
"A362559",
"A363532",
"A363619",
"A363620",
"A363621",
"A363622",
"A363623",
"A363624",
"A363625",
"A363626"
]
| null | Gus Wiseman, Jun 14 2023 | 2023-06-15T20:06:40 | oeisdata/seq/A363/A363532.seq | b2c2454025768181f3c46678531de97a |
A363533 | Least k such that n*F(k)+1 is prime, where F = A000045 is the Fibonacci sequence, or -1 if no such k exists. | [
"1",
"1",
"3",
"1",
"3",
"1",
"9",
"3",
"3",
"1",
"3",
"1",
"9",
"3",
"3",
"1",
"6",
"1",
"9",
"3",
"3",
"1",
"3",
"4",
"18",
"3",
"9",
"1",
"3",
"1",
"15",
"4",
"3",
"4",
"3",
"1",
"9",
"5",
"3",
"1",
"3",
"1",
"48",
"3",
"9",
"1",
"24",
"3",
"9",
"3",
"3",
"1",
"3",
"3",
"9",
"3",
"6",
"1",
"24",
"1",
"36",
"5",
"3",
"4",
"3",
"1",
"12",
"3",
"3",
"1",
"6",
"1",
"12",
"3",
"3",
"4",
"6",
"1",
"9",
"4",
"3",
"1",
"3",
"5"
]
| [
"nonn"
]
| 15 | 1 | 3 | [
"A000045",
"A034693",
"A124067",
"A361902",
"A362376",
"A363533",
"A363534",
"A363535",
"A363536"
]
| null | Pontus von Brömssen, Jun 09 2023 | 2023-06-22T10:41:04 | oeisdata/seq/A363/A363533.seq | 1ecd472e0dce8906bd82bafbaef4aa02 |
A363534 | Records in A363533. | [
"1",
"3",
"9",
"18",
"48",
"60",
"540",
"1998",
"2844",
"3045",
"39753"
]
| [
"nonn",
"more"
]
| 7 | 1 | 2 | [
"A361997",
"A363533",
"A363534",
"A363535"
]
| null | Pontus von Brömssen, Jun 09 2023 | 2023-06-19T17:38:39 | oeisdata/seq/A363/A363534.seq | 1de0c1d33810d797f52426b6714cbe6f |
A363535 | Indices of records in A363533. | [
"1",
"3",
"7",
"25",
"43",
"139",
"227",
"263",
"727",
"2463",
"3541"
]
| [
"nonn",
"more"
]
| 10 | 1 | 2 | [
"A361998",
"A363533",
"A363534",
"A363535"
]
| null | Pontus von Brömssen, Jun 09 2023 | 2023-06-19T17:38:31 | oeisdata/seq/A363/A363535.seq | d53d0ee4a03882c4aa0e373b9df48f14 |
A363536 | a(n) is the smallest k such that A363533(k) = n, or -1 if no such k exists. | [
"1",
"-1",
"3",
"24",
"38",
"17",
"142",
"248",
"7",
"328",
"528",
"67",
"446",
"1676",
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"208",
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"181",
"4388",
"18694",
"383",
"22754",
"23836",
"43",
"8212",
"34636"
]
| [
"sign"
]
| 4 | 1 | 3 | [
"A361999",
"A363533",
"A363536"
]
| null | Pontus von Brömssen, Jun 09 2023 | 2023-07-15T06:35:52 | oeisdata/seq/A363/A363536.seq | 3a800f0182b3087857c9124aa6bdf732 |
A363537 | Rewrite A087980(n) = Product_{i=1..m} p(i)^e(i) instead as Sum_{i=1..m} 2^(i-1), where m = omega(A087980(n)) = A001221(A087980(n)). | [
"0",
"1",
"2",
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"64",
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"259",
"4097",
"41",
"516",
"80",
"16384",
"133",
"2050",
"264",
"38"
]
| [
"nonn"
]
| 6 | 1 | 3 | [
"A000079",
"A001221",
"A006939",
"A087980",
"A362227",
"A363537"
]
| null | Michael De Vlieger, Jun 09 2023 | 2023-06-11T12:29:33 | oeisdata/seq/A363/A363537.seq | c2c889e3d231a1070d3a6d0dc963b58e |
A363538 | Decimal expansion of Sum_{k>=1} (H(k) - log(k) - gamma)/k, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number and gamma is Euler's constant (A001620). | [
"7",
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"0",
"4",
"5",
"5",
"9"
]
| [
"nonn",
"cons"
]
| 10 | 0 | 1 | [
"A001008",
"A001620",
"A002805",
"A072691",
"A082633",
"A363538",
"A363539",
"A363540"
]
| null | Amiram Eldar, Jun 09 2023 | 2025-04-27T03:22:54 | oeisdata/seq/A363/A363538.seq | 123b661f53629fa612087496e59d9bc3 |
A363539 | Decimal expansion of Sum_{k>=1} (H(k)^2 - (log(k) + gamma)^2)/k, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number and gamma is Euler's constant (A001620). | [
"1",
"9",
"6",
"8",
"9",
"6",
"9",
"0",
"8",
"3",
"9",
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"4",
"4",
"0",
"9",
"8",
"7",
"8",
"3"
]
| [
"nonn",
"cons"
]
| 5 | 1 | 2 | [
"A001008",
"A001620",
"A002117",
"A002805",
"A082633",
"A086279",
"A363538",
"A363539",
"A363540"
]
| null | Amiram Eldar, Jun 09 2023 | 2023-06-09T01:30:52 | oeisdata/seq/A363/A363539.seq | a9f07666b2910658372c4e618fe7fb8b |
A363540 | Decimal expansion of Sum_{k>=1} (H(k)^3 - (log(k) + gamma)^3)/k, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number and gamma is Euler's constant (A001620). | [
"5",
"8",
"2",
"1",
"7",
"4",
"0",
"0",
"8",
"5",
"0",
"4",
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"6",
"4",
"6",
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"8",
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"3",
"1",
"9",
"0",
"9",
"6",
"5",
"9",
"7"
]
| [
"nonn",
"cons"
]
| 5 | 1 | 1 | [
"A001008",
"A001620",
"A002117",
"A013662",
"A082633",
"A086279",
"A086280",
"A363538",
"A363539",
"A363540"
]
| null | Amiram Eldar, Jun 09 2023 | 2023-06-09T01:30:15 | oeisdata/seq/A363/A363540.seq | 803962f10191b795a57fb2fb32c7ef0d |
A363541 | G.f. satisfies A(x) = exp( Sum_{k>=1} (3^k + A(x^k)) * x^k/k ). | [
"1",
"4",
"17",
"73",
"324",
"1469",
"6838",
"32490",
"157398",
"775010",
"3870690",
"19567202",
"99957231",
"515250057",
"2676884745",
"14002926871",
"73693381322",
"389904743248",
"2072794614996",
"11066421965311",
"59310040841395",
"318978744562253",
"1720962766007827"
]
| [
"nonn"
]
| 19 | 0 | 2 | [
"A001678",
"A036249",
"A362389",
"A363507",
"A363541",
"A363543",
"A363546"
]
| null | Seiichi Manyama, Jun 09 2023 | 2023-06-10T10:56:16 | oeisdata/seq/A363/A363541.seq | 6e22321932c16b2143c255474565c56b |
A363542 | G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * (2^k + A(x^k)) * x^k/k ). | [
"1",
"3",
"5",
"14",
"38",
"114",
"360",
"1166",
"3872",
"13094",
"44961",
"156244",
"548636",
"1943333",
"6935817",
"24917586",
"90039163",
"327029681",
"1193258619",
"4371901789",
"16077606949",
"59325057056",
"219579151797",
"815017718383",
"3032959638204",
"11313632991360",
"42295634914403"
]
| [
"nonn"
]
| 10 | 0 | 2 | [
"A038075",
"A362389",
"A363542",
"A363543"
]
| null | Seiichi Manyama, Jun 09 2023 | 2023-06-09T08:54:19 | oeisdata/seq/A363/A363542.seq | b39529eec241613dca39567ff6614c0c |
A363543 | G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * (3^k + A(x^k)) * x^k/k ). | [
"1",
"4",
"7",
"23",
"69",
"234",
"826",
"3000",
"11168",
"42313",
"162829",
"634052",
"2495051",
"9903761",
"39612048",
"159481988",
"645833656",
"2628829700",
"10749777653",
"44139474552",
"181916530895",
"752288709592",
"3120574260606",
"12981015704961",
"54138655342763",
"226330448292140"
]
| [
"nonn"
]
| 9 | 0 | 2 | [
"A038075",
"A363509",
"A363541",
"A363542",
"A363543"
]
| null | Seiichi Manyama, Jun 09 2023 | 2023-06-09T08:54:23 | oeisdata/seq/A363/A363543.seq | 8a80b11753d5c6c50657ae1b25df6adc |
A363544 | Least prime p such that 2n can be written as the sum or absolute difference of p and the next prime, or -1 if no such prime exists. | [
"-1",
"3",
"7",
"23",
"3",
"139",
"5",
"113",
"1831",
"7",
"887",
"1129",
"11",
"2477",
"2971",
"13",
"5591",
"1327",
"17",
"30593",
"19333",
"19",
"15683",
"81463",
"28229",
"31907",
"23",
"35617",
"82073",
"44293",
"29",
"34061",
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"162143",
"31",
"173359",
"31397",
"404597",
"212701",
"37",
"542603",
"265621",
"41",
"155921",
"544279",
"43",
"927869",
"1100977"
]
| [
"sign"
]
| 32 | 0 | 2 | [
"A000040",
"A000230",
"A001043",
"A001223",
"A327467",
"A359199",
"A362465",
"A363544"
]
| null | Karl-Heinz Hofmann and Peter Munn, Jun 09 2023 | 2023-07-06T16:57:28 | oeisdata/seq/A363/A363544.seq | 93cc1bbf5fe27ce2a6c206b9d2d52490 |
A363545 | G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * x^k/(k * (1 - 2*x^k)) ). | [
"1",
"1",
"4",
"14",
"54",
"206",
"823",
"3312",
"13619",
"56643",
"238569",
"1014443",
"4352038",
"18809992",
"81843021",
"358186642",
"1575810191",
"6965004499",
"30914431131",
"137736012285",
"615785575785",
"2761693248028",
"12421390811559",
"56016050571825",
"253228531426237"
]
| [
"nonn"
]
| 20 | 0 | 3 | [
"A052855",
"A198518",
"A362389",
"A363545",
"A363546",
"A363580",
"A363581"
]
| null | Seiichi Manyama, Jun 09 2023 | 2023-06-10T10:55:52 | oeisdata/seq/A363/A363545.seq | f5b19c3c7b47a04a70bc644d99f1a4c7 |
A363546 | G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * x^k/(k * (1 - 3*x^k)) ). | [
"1",
"1",
"5",
"22",
"105",
"497",
"2431",
"11976",
"59928",
"302816",
"1545660",
"7955132",
"41255625",
"215378364",
"1131134574",
"5972272636",
"31684600709",
"168824599282",
"903080385252",
"4848038120323",
"26110774945462",
"141048622038068",
"764026532321068",
"4149020129689451"
]
| [
"nonn"
]
| 17 | 0 | 3 | [
"A052855",
"A198518",
"A363541",
"A363545",
"A363546",
"A363580",
"A363581"
]
| null | Seiichi Manyama, Jun 09 2023 | 2023-06-10T10:55:56 | oeisdata/seq/A363/A363546.seq | 413b146c6715c75e0f739f3b93bcf511 |
A363547 | G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * x^k/(k * (1 - x^k)^2) ). | [
"1",
"1",
"4",
"13",
"47",
"168",
"635",
"2420",
"9460",
"37445",
"150309",
"609568",
"2495710",
"10298332",
"42793974",
"178910161",
"752034697",
"3176346092",
"13473881397",
"57378127986",
"245205968960",
"1051257068207",
"4520229295852",
"19488595397346",
"84231899582543",
"364893870958302"
]
| [
"nonn"
]
| 14 | 0 | 3 | [
"A029857",
"A052855",
"A363545",
"A363547",
"A363548"
]
| null | Seiichi Manyama, Jun 09 2023 | 2023-06-09T15:05:02 | oeisdata/seq/A363/A363547.seq | 02781bc83a426d54cd82e76a1c7b428b |
A363548 | G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * x^k/(k * (1 - x^k)^3) ). | [
"1",
"1",
"5",
"19",
"79",
"326",
"1414",
"6198",
"27794",
"126233",
"580885",
"2700135",
"12665756",
"59869222",
"284919675",
"1364009722",
"6564545500",
"31742029545",
"154134718727",
"751316355122",
"3674923035139",
"18031965040197",
"88734141475113",
"437813286219942",
"2165445447313147"
]
| [
"nonn"
]
| 13 | 0 | 3 | [
"A052855",
"A363507",
"A363546",
"A363547",
"A363548"
]
| null | Seiichi Manyama, Jun 09 2023 | 2023-06-09T15:05:07 | oeisdata/seq/A363/A363548.seq | 2438a8ecc43123583fce7796d21ab058 |
A363549 | Total number of parity changes within all partitions of [n]. | [
"0",
"0",
"2",
"9",
"35",
"152",
"690",
"3476",
"18362",
"105507",
"633439",
"4077386",
"27317322",
"194202164",
"1431942154",
"11117639073",
"89255122863",
"750051307896",
"6500488706254",
"58693723144324",
"545325034579386",
"5258317906940219",
"52072378163037347",
"533479904210984930",
"5603461526474415150"
]
| [
"nonn"
]
| 17 | 0 | 3 | [
"A000110",
"A363496",
"A363519",
"A363549"
]
| null | Alois P. Heinz, Jun 09 2023 | 2023-06-12T17:25:11 | oeisdata/seq/A363/A363549.seq | 1715813872f1b8361c595541a48cf209 |
A363550 | Number of partitions of [n] having exactly one parity change within the partition. | [
"0",
"0",
"2",
"1",
"3",
"2",
"7",
"5",
"20",
"15",
"67",
"52",
"255",
"203",
"1080",
"877",
"5017",
"4140",
"25287",
"21147",
"137122",
"115975",
"794545",
"678570",
"4892167",
"4213597",
"31858034",
"27644437",
"218543759",
"190899322",
"1573857867",
"1382958545",
"11863100692",
"10480142147",
"93345011951",
"82864869804"
]
| [
"nonn"
]
| 14 | 0 | 3 | [
"A000110",
"A011968",
"A363519",
"A363550"
]
| null | Alois P. Heinz, Jun 09 2023 | 2023-06-09T19:05:28 | oeisdata/seq/A363/A363550.seq | c8f32b6fc5daf7f7c1b80e3714e57bec |
A363551 | Möbius function of rank 3: a(n) = lambda(n) = A008836(n) if n is cubefree and 0 otherwise. | [
"1",
"-1",
"-1",
"1",
"-1",
"1",
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"1",
"-1",
"-1",
"0",
"-1",
"1",
"-1"
]
| [
"sign",
"mult",
"easy"
]
| 13 | 1 | null | [
"A004709",
"A008683",
"A008836",
"A046099",
"A053864",
"A053865",
"A053981",
"A189021",
"A189022",
"A189023",
"A212793",
"A299406",
"A307420",
"A363551",
"A363552",
"A363553"
]
| null | Amiram Eldar, Jun 10 2023 | 2023-06-11T02:57:25 | oeisdata/seq/A363/A363551.seq | 4e5cab4bed23150a803e58052e05e474 |
A363552 | Möbius function of rank 4: a(n) = lambda(n) = A008836(n) if n is biquadratefree (A046100) and 0 otherwise. | [
"1",
"-1",
"-1",
"1",
"-1",
"1",
"-1",
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"-1",
"1",
"-1",
"1",
"-1",
"0",
"1",
"-1",
"-1",
"-1",
"1",
"-1",
"-1",
"-1",
"-1",
"1",
"-1"
]
| [
"sign",
"mult",
"easy"
]
| 11 | 1 | null | [
"A008683",
"A008836",
"A046100",
"A053864",
"A053865",
"A053981",
"A157295",
"A189021",
"A189022",
"A189023",
"A307430",
"A353519",
"A363551",
"A363552",
"A363553"
]
| null | Amiram Eldar, Jun 10 2023 | 2023-06-11T02:57:30 | oeisdata/seq/A363/A363552.seq | d691ba88e058ae42b653d22621cd1f2b |
A363553 | Möbius function of rank 5: a(n) = lambda(n) = A008836(n) if n is 5-free and 0 otherwise. | [
"1",
"-1",
"-1",
"1",
"-1",
"1",
"-1",
"-1",
"1",
"1",
"-1",
"-1",
"-1",
"1",
"1",
"1",
"-1",
"-1",
"-1",
"-1",
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"1",
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"1",
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"-1",
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"1",
"1",
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"1",
"-1",
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"-1",
"0",
"1",
"-1",
"-1",
"-1",
"1",
"-1",
"-1",
"-1",
"-1",
"1"
]
| [
"sign",
"mult",
"easy"
]
| 11 | 1 | null | [
"A008836",
"A053864",
"A053865",
"A053981",
"A189021",
"A189022",
"A189023",
"A363551",
"A363552",
"A363553"
]
| null | Amiram Eldar, Jun 10 2023 | 2023-06-11T02:57:33 | oeisdata/seq/A363/A363553.seq | 0b4e9fa7f6b26e9fa477f64a16dc5c44 |
A363554 | a(1) = 1; for n > 1, a(n) is the smallest positive integer such that both the gradients and y-intercepts of the lines between any two points (i, a(i)) and (j, a(j)) are distinct. | [
"1",
"1",
"2",
"5",
"11",
"4",
"3",
"18",
"26",
"35",
"48",
"66",
"16",
"99",
"129",
"27",
"67",
"149",
"190",
"8",
"235",
"259",
"285",
"348",
"276",
"34",
"24",
"97",
"362",
"170",
"155",
"15",
"504",
"464",
"9",
"639",
"449",
"173",
"391",
"768",
"577",
"682",
"836",
"937",
"598",
"438",
"94",
"6",
"1063",
"1007",
"500",
"210",
"1146",
"1303",
"1390",
"806",
"1530",
"62",
"1096",
"1739",
"212",
"28",
"1001",
"1380"
]
| [
"nonn"
]
| 11 | 1 | 3 | [
"A229037",
"A236335",
"A286091",
"A363554"
]
| null | Scott R. Shannon, Jun 10 2023 | 2023-07-03T09:16:58 | oeisdata/seq/A363/A363554.seq | bf1596e2c89b4b828c35dfe5304b4276 |
A363555 | Expansion of g.f. A(x) satisfying 0 = Sum_{n>=0} (-1)^n * x^(n*(n-1)/2) * A(x)^(n*(n+1)/2) / Product_{k=2..n+2} (1 - x^k*A(x)^(k+1)). | [
"1",
"1",
"3",
"10",
"39",
"163",
"719",
"3291",
"15495",
"74568",
"365188",
"1814220",
"9120733",
"46316195",
"237229711",
"1224150186",
"6358008567",
"33211790566",
"174368764180",
"919634519638",
"4870040209108",
"25885098736539",
"138044748197031",
"738439479552465",
"3961167293262753",
"21303283844252223"
]
| [
"nonn"
]
| 30 | 0 | 3 | [
"A082395",
"A363555",
"A363556"
]
| null | Paul D. Hanna, Jul 09 2023 | 2023-07-20T10:06:28 | oeisdata/seq/A363/A363555.seq | 9e73cbc793ffa62c70ebc1fb8a3f02dc |
A363556 | Expansion of g.f. A(x) satisfying 0 = Sum_{n>=0} (-1)^n * x^(n*(n-1)/2) * A(x)^(n^2) / Product_{k=2..n+2} (1 - x^k*A(x)^(2*k+1)). | [
"1",
"1",
"4",
"20",
"116",
"729",
"4835",
"33308",
"236040",
"1709710",
"12601576",
"94209348",
"712665643",
"5445033052",
"41957720686",
"325702058100",
"2544612673624",
"19993230400674",
"157880283331190",
"1252345341860312",
"9974116387535508",
"79727867712667593",
"639419309923767255",
"5143690907082615272"
]
| [
"nonn"
]
| 16 | 0 | 3 | [
"A082395",
"A363555",
"A363556"
]
| null | Paul D. Hanna, Jul 09 2023 | 2023-07-20T10:07:00 | oeisdata/seq/A363/A363556.seq | 4c4db6ff3e983105fbae3d0d4d6c2656 |
A363557 | Expansion of g.f. A(x) satisfying 0 = Sum_{n>=0} (-1)^n * x^(n*(n-1)/2) * A(x)^n / Product_{k=1..n+1} (1 - x^k). | [
"1",
"1",
"1",
"2",
"4",
"9",
"20",
"47",
"112",
"273",
"677",
"1702",
"4330",
"11128",
"28847",
"75341",
"198066",
"523713",
"1391869",
"3716098",
"9962252",
"26806275",
"72372721",
"195994320",
"532266707",
"1449216287",
"3955193019",
"10818202369",
"29650108510",
"81417795070",
"223964216673",
"617097850848",
"1702943168118"
]
| [
"nonn"
]
| 9 | 0 | 4 | [
"A082395",
"A363555",
"A363557"
]
| null | Paul D. Hanna, Jul 11 2023 | 2023-07-20T10:07:15 | oeisdata/seq/A363/A363557.seq | b4e89119a8e3ae10237dff0c638b9675 |
A363558 | Expansion of g.f. A(x) = Sum_{n=-oo..+oo} x^n * (2 + x^n)^(2*n). | [
"1",
"5",
"16",
"77",
"256",
"1104",
"4121",
"16832",
"65536",
"264688",
"1048617",
"4205568",
"16779008",
"67162112",
"268436016",
"1073999165",
"4294967296",
"17180983296",
"68719549696",
"274882887680",
"1099511628896",
"4398068904021",
"17592186086656",
"70368840646656",
"281474978676736",
"1125900326286464"
]
| [
"nonn"
]
| 17 | 0 | 2 | [
"A260147",
"A363558",
"A363559",
"A363561",
"A363569"
]
| null | Paul D. Hanna, Aug 01 2023 | 2023-08-07T08:04:01 | oeisdata/seq/A363/A363558.seq | 81082b128172aeeccc3344fc8aed6b11 |
A363559 | Expansion of g.f. A(x) = Sum_{n=-oo..+oo} x^n * (3 + x^n)^(2*n). | [
"1",
"10",
"81",
"757",
"6561",
"59454",
"531496",
"4788072",
"43046721",
"387480753",
"3486784492",
"31381709148",
"282429556893",
"2541872737062",
"22876792457796",
"205891204134565",
"1853020188851841",
"16677182431460826",
"150094635300957591",
"1350851725033981380",
"12157665459056934471"
]
| [
"nonn"
]
| 17 | 0 | 2 | [
"A260147",
"A363558",
"A363559",
"A363561",
"A363569"
]
| null | Paul D. Hanna, Aug 01 2023 | 2023-08-07T08:04:06 | oeisdata/seq/A363/A363559.seq | 247650fdc278f5fb94d193acb4465723 |
A363560 | Expansion of g.f. A(x) satisfying A(x)^3 = 1 + x*(A(x) + A(x)^2 + A(x)^9). | [
"1",
"1",
"3",
"18",
"126",
"966",
"7863",
"66696",
"583111",
"5217513",
"47547405",
"439777242",
"4117802109",
"38956162023",
"371795456373",
"3575401032544",
"34611064585803",
"336998629754631",
"3298200003722997",
"32428037256038775",
"320151289224740949",
"3172536384239678856",
"31544584654878015766"
]
| [
"nonn"
]
| 17 | 0 | 3 | [
"A161634",
"A300048",
"A363560"
]
| null | Paul D. Hanna, Aug 12 2023 | 2023-08-16T10:26:23 | oeisdata/seq/A363/A363560.seq | ebe5bc5be6f25e1096c5991ee1e4029b |
A363561 | G.f.: Sum_{n=-oo..+oo} x^n * (sqrt(2) + x^n)^(2*n). | [
"1",
"3",
"4",
"15",
"16",
"52",
"77",
"184",
"256",
"716",
"1045",
"2400",
"4320",
"9024",
"16524",
"35439",
"65536",
"135424",
"264928",
"534016",
"1048856",
"2124523",
"4196944",
"8435712",
"16792576",
"33658512",
"67118016",
"134478584",
"268435513",
"537346048",
"1073876144",
"2148499456",
"4294967296",
"8592337520",
"17179956224",
"34364358760"
]
| [
"nonn"
]
| 17 | 0 | 2 | [
"A260147",
"A363558",
"A363559",
"A363561",
"A363569"
]
| null | Paul D. Hanna, Aug 01 2023 | 2023-08-07T08:03:56 | oeisdata/seq/A363/A363561.seq | e74c1fe5775e4592d37ad537a3850889 |
A363562 | Expansion of g.f. A(x) satisfying 1 = Sum_{n>=0} x^n * A(x)^n / (1 + x^(n+1)*A(x)^2). | [
"1",
"2",
"7",
"32",
"165",
"915",
"5321",
"32013",
"197589",
"1244127",
"7960163",
"51604376",
"338235709",
"2237671348",
"14922662524",
"100210165389",
"677048764444",
"4598998298373",
"31389535211441",
"215163326541577",
"1480569995180206",
"10223713874584005",
"70822394367021543",
"492034480142649446"
]
| [
"nonn"
]
| 9 | 0 | 2 | [
"A340329",
"A340355",
"A363562",
"A363563",
"A363564"
]
| null | Paul D. Hanna, Jul 19 2023 | 2023-07-20T10:07:31 | oeisdata/seq/A363/A363562.seq | 6db5eba20e6c281362132c461133fa75 |
A363563 | Expansion of g.f. A(x) satisfying 1 = Sum_{n>=0} x^n * A(x)^(2*n) / (1 + x^(n+1)*A(x)^3). | [
"1",
"2",
"11",
"84",
"738",
"7029",
"70570",
"735401",
"7879118",
"86249454",
"960434270",
"10845322135",
"123896322956",
"1429327711980",
"16628329185358",
"194858230552674",
"2297972689389087",
"27252117638208701",
"324797817830706494",
"3888255542301372866",
"46733817274361827340",
"563736664663891455990"
]
| [
"nonn"
]
| 9 | 0 | 2 | [
"A340329",
"A340355",
"A363562",
"A363563",
"A363564"
]
| null | Paul D. Hanna, Jul 19 2023 | 2023-07-20T10:07:48 | oeisdata/seq/A363/A363563.seq | 764a7fd96f864a979d17bfdb050ad5cb |
A363564 | Expansion of g.f. A(x) satisfying 1 = Sum_{n>=0} x^n * A(x)^(3*n) / (1 + x^(n+1)*A(x)^4). | [
"1",
"2",
"15",
"160",
"1979",
"26633",
"378612",
"5593669",
"85036458",
"1321547904",
"20901013044",
"335307963490",
"5443261450865",
"89249920538306",
"1475910492040246",
"24587479259900805",
"412252774520658173",
"6951447807236206940",
"117807212665434783089",
"2005490388805271264356"
]
| [
"nonn"
]
| 9 | 0 | 2 | [
"A340329",
"A340355",
"A363562",
"A363563",
"A363564"
]
| null | Paul D. Hanna, Jul 19 2023 | 2023-07-20T10:08:09 | oeisdata/seq/A363/A363564.seq | 41c23a9ddeb69290288b4ba3a34b3a35 |
A363565 | G.f. satisfies A(x) = exp( Sum_{k>=1} (2 * (-1)^k + A(x^k)) * x^k/k ). | [
"1",
"-1",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"1",
"1",
"0",
"1",
"2",
"2",
"1",
"3",
"5",
"4",
"4",
"10",
"13",
"11",
"16",
"30",
"34",
"35",
"58",
"91",
"99",
"123",
"200",
"275",
"315",
"437",
"671",
"869",
"1065",
"1548",
"2239",
"2848",
"3730",
"5446",
"7530",
"9699",
"13273",
"19056",
"25730",
"33947",
"47463",
"66796",
"89565",
"120976",
"170033",
"235524"
]
| [
"sign"
]
| 10 | 0 | 14 | [
"A001678",
"A363565",
"A363566",
"A363567"
]
| null | Seiichi Manyama, Jun 10 2023 | 2023-06-10T11:18:21 | oeisdata/seq/A363/A363565.seq | ee3ba353929d55c8c92548ad752e2880 |
A363566 | G.f. satisfies A(x) = exp( Sum_{k>=1} (3 * (-1)^k + A(x^k)) * x^k/k ). | [
"1",
"-2",
"2",
"0",
"-2",
"0",
"5",
"-3",
"-9",
"11",
"16",
"-34",
"-27",
"102",
"30",
"-296",
"56",
"807",
"-548",
"-2056",
"2572",
"4770",
"-9846",
"-9351",
"33822",
"11496",
"-107296",
"17853",
"316498",
"-210013",
"-862785",
"1069352",
"2122294",
"-4347217",
"-4402138",
"15657617",
"5883290",
"-51677928",
"7420844",
"157867636"
]
| [
"sign"
]
| 9 | 0 | 2 | [
"A001678",
"A363509",
"A363565",
"A363566",
"A363575"
]
| null | Seiichi Manyama, Jun 10 2023 | 2023-06-10T11:18:26 | oeisdata/seq/A363/A363566.seq | 1fd7f087e7a3a2b6e4fb19f3a5170151 |
A363567 | G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * x^k/(k * (1 + x^k)^2) ). | [
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"2",
"1",
"1",
"3",
"3",
"2",
"4",
"7",
"7",
"7",
"12",
"17",
"17",
"22",
"37",
"47",
"51",
"73",
"110",
"133",
"162",
"242",
"339",
"412",
"545",
"798",
"1065",
"1342",
"1860",
"2648",
"3474",
"4547",
"6400",
"8874",
"11665",
"15754",
"22152",
"30205",
"40201",
"55301",
"77115",
"104463",
"141087",
"195669",
"270620",
"366902"
]
| [
"nonn"
]
| 9 | 0 | 8 | [
"A198518",
"A363547",
"A363565",
"A363567",
"A363575"
]
| null | Seiichi Manyama, Jun 10 2023 | 2023-06-10T11:18:16 | oeisdata/seq/A363/A363567.seq | 355c7ac2020e4ddc5029907ce1e6322d |
A363568 | Expansion of l.g.f. A(x) satisfying theta_4(x) = Sum_{n=-oo..+oo} x^n * (2*exp(A(x)) - x^n)^(n-1) where theta_4(x) = Sum_{n=-oo..+oo} (-1)^n * x^(n^2) is a Jacobi theta function. | [
"2",
"18",
"152",
"1298",
"11432",
"102528",
"931968",
"8554698",
"79116722",
"736053548",
"6880854312",
"64581401504",
"608178222316",
"5743797385400",
"54380418647072",
"515969530624186",
"4904912090029220",
"46705792266725778",
"445414424602046360",
"4253490292103734268",
"40668438064085218644",
"389270517755459345232"
]
| [
"nonn"
]
| 13 | 1 | 1 | [
"A002448",
"A363568",
"A363574"
]
| null | Paul D. Hanna, Jun 11 2023 | 2023-11-18T07:58:21 | oeisdata/seq/A363/A363568.seq | 3c75acad4c469875d3b1077a4f9dec0b |
A363569 | Expansion of g.f. A(x) = Sum_{n=-oo..+oo} x^n * (i + x^n)^(2*n), where i^2 = -1. | [
"1",
"0",
"1",
"-3",
"1",
"4",
"-4",
"-8",
"1",
"23",
"-8",
"-12",
"-27",
"12",
"36",
"15",
"1",
"16",
"-149",
"-20",
"71",
"91",
"166",
"-24",
"-119",
"-186",
"-285",
"251",
"-26",
"28",
"761",
"-32",
"1",
"-199",
"-679",
"-827",
"-310",
"36",
"970",
"1572",
"1821",
"40",
"-2631",
"-44",
"331",
"-5628",
"1772",
"-48",
"-495",
"3051",
"2546",
"6697",
"-1715",
"52",
"2791",
"-7425",
"-8007",
"-10869",
"-3653",
"-60"
]
| [
"sign"
]
| 20 | 0 | 4 | [
"A260147",
"A363558",
"A363559",
"A363569"
]
| null | Paul D. Hanna, Jul 31 2023 | 2023-08-07T12:51:04 | oeisdata/seq/A363/A363569.seq | fa3b9e801c4e64b7161eb5d5130d5ed7 |
A363570 | Expansion of (1 / sqrt(1 - 8*x + 4*x^2) - 1 / (1 - x)) / 3. | [
"0",
"1",
"7",
"45",
"295",
"1981",
"13545",
"93829",
"656311",
"4625181",
"32788657",
"233567269",
"1670457321",
"11987269477",
"86268665917",
"622391877045",
"4500029549911",
"32598283556317",
"236542093805025",
"1719008077215205",
"12509403045819505",
"91143878730342021",
"664816240262272237"
]
| [
"nonn"
]
| 9 | 0 | 3 | [
"A030662",
"A047665",
"A069835",
"A098663",
"A363570",
"A363571"
]
| null | Ilya Gutkovskiy, Aug 17 2023 | 2023-08-24T10:33:12 | oeisdata/seq/A363/A363570.seq | 9a8cdddc0ea139f924becb40d00c88ab |
A363571 | Expansion of (1 / sqrt(1 - 10*x + 9*x^2) - 1 / (1 - x)) / 4. | [
"0",
"1",
"8",
"61",
"480",
"3881",
"31976",
"266981",
"2251136",
"19124881",
"163452168",
"1403748941",
"12104113632",
"104723793721",
"908680775528",
"7904234296181",
"68905275700736",
"601832985410081",
"5265459181363976",
"46137526574521181",
"404821208100919520",
"3556361565584509001"
]
| [
"nonn"
]
| 8 | 0 | 3 | [
"A030662",
"A047665",
"A084771",
"A098665",
"A363570",
"A363571"
]
| null | Ilya Gutkovskiy, Aug 17 2023 | 2023-08-24T10:33:23 | oeisdata/seq/A363/A363571.seq | 300177154dec84dd380d1ead420ec9d8 |
A363572 | Lexicographically earliest sequence of distinct terms > 0 such that the concatenation of the rightmost digit of a(n) and the leftmost digit of a(n+1) forms a prime number. The rightmost digit of a(n) cannot be 0. | [
"1",
"3",
"7",
"9",
"71",
"11",
"12",
"31",
"13",
"14",
"15",
"32",
"33",
"16",
"17",
"18",
"34",
"19",
"72",
"35",
"36",
"73",
"74",
"37",
"38",
"39",
"75",
"91",
"76",
"77",
"92",
"93",
"78",
"94",
"79",
"701",
"95",
"96",
"101",
"97",
"98",
"99",
"702",
"301",
"102",
"302",
"303",
"103",
"104",
"105",
"304",
"106",
"107",
"108",
"305",
"306",
"109",
"703",
"111",
"112",
"307",
"113",
"114",
"115"
]
| [
"base",
"nonn"
]
| 17 | 1 | 2 | [
"A152607",
"A363572"
]
| null | Eric Angelini, Aug 17 2023 | 2024-03-09T08:19:09 | oeisdata/seq/A363/A363572.seq | 08d4d5140a0d22b365ce9a319306c698 |
A363573 | Expansion of g.f. A(x) satisfying A(x) = 1 + x*(A(x) - A(x)^3 + A(x)^5). | [
"1",
"1",
"3",
"16",
"99",
"670",
"4804",
"35855",
"275635",
"2167577",
"17354844",
"140994899",
"1159398760",
"9631155422",
"80703507043",
"681333999628",
"5789823864323",
"49484286592503",
"425092050147999",
"3668385302806058",
"31786451503719132",
"276447315011186576",
"2412336247105063011",
"21114946136742383146"
]
| [
"nonn"
]
| 9 | 0 | 3 | [
"A161634",
"A219537",
"A271469",
"A300048",
"A363560",
"A363573"
]
| null | Paul D. Hanna, Aug 14 2023 | 2023-08-15T18:52:31 | oeisdata/seq/A363/A363573.seq | 8a39434dc323239e165b71fcacc04c2c |
A363574 | Expansion of g.f. A(x) satisfying theta_4(x) = Sum_{n=-oo..+oo} x^n * (2*A(x) - x^n)^(n-1) where theta_4(x) = Sum_{n=-oo..+oo} (-1)^n * x^(n^2) is a Jacobi theta function. | [
"1",
"2",
"11",
"70",
"485",
"3586",
"27702",
"221044",
"1807751",
"15073208",
"127658948",
"1095160206",
"9496825919",
"83109648780",
"733063257227",
"6510317010502",
"58166005554886",
"522446273512866",
"4714846241261093",
"42730135199777198",
"388741207648594732",
"3548875263271057666",
"32500492203726887011"
]
| [
"nonn"
]
| 17 | 0 | 2 | [
"A002448",
"A028982",
"A357227",
"A363568",
"A363574"
]
| null | Paul D. Hanna, Jun 10 2023 | 2023-11-18T07:58:10 | oeisdata/seq/A363/A363574.seq | 427253f249067551cc0e41a15886dd23 |
A363575 | G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * x^k/(k * (1 + x^k)^3) ). | [
"1",
"1",
"-1",
"1",
"2",
"-4",
"-1",
"10",
"-3",
"-20",
"19",
"38",
"-70",
"-65",
"221",
"73",
"-640",
"117",
"1745",
"-1223",
"-4433",
"5770",
"10124",
"-22007",
"-18999",
"75063",
"19307",
"-235725",
"59665",
"685744",
"-525477",
"-1832544",
"2531982",
"4364936",
"-10007555",
"-8468154",
"35302510",
"8542655",
"-114305453"
]
| [
"sign"
]
| 8 | 0 | 5 | [
"A198518",
"A363548",
"A363566",
"A363567",
"A363575"
]
| null | Seiichi Manyama, Jun 10 2023 | 2023-06-10T11:18:30 | oeisdata/seq/A363/A363575.seq | 3189c645303dde40c836824170c968ab |
A363576 | a(1) = 1, a(2) = 6; for n > 2, a(n) is the smallest positive number that has not yet appeared such that a(n) has a common factor with a(n-1), has no common factor with a(n-2), while the difference |a(n) - a(n-1)| is distinct from all previous differences |a(i) - a(i-1)|, i=2..n-1. | [
"1",
"6",
"10",
"35",
"21",
"12",
"20",
"55",
"33",
"18",
"28",
"77",
"143",
"26",
"14",
"105",
"51",
"34",
"40",
"95",
"57",
"24",
"22",
"187",
"85",
"15",
"36",
"52",
"65",
"45",
"42",
"68",
"221",
"39",
"63",
"56",
"38",
"171",
"75",
"115",
"46",
"74",
"111",
"69",
"92",
"44",
"165",
"87",
"58",
"88",
"99",
"135",
"50",
"82",
"123",
"183",
"122",
"70",
"133",
"209",
"66",
"93",
"155",
"80",
"114",
"153",
"391",
"161",
"84"
]
| [
"nonn"
]
| 7 | 1 | 2 | [
"A098550",
"A336957",
"A360519",
"A361102",
"A363576"
]
| null | Scott R. Shannon, Jun 10 2023 | 2023-08-14T08:29:42 | oeisdata/seq/A363/A363576.seq | 0fe34c6a65627e6a5966ce4c4dbd2d0c |
A363577 | Number of inequivalent Hamiltonian paths starting in the lower left corner of an n X n grid graph (paths differing only by rotations and reflections are regarded as equivalent). | [
"1",
"1",
"3",
"23",
"347",
"10199",
"683227",
"85612967",
"25777385143",
"14396323278040",
"19799561204761862",
"50351228336401026361",
"319210377672595552740369",
"3736517399241599771428011100",
"109790442395888863208285555153329",
"5952238893391106787883489313797219949"
]
| [
"nonn",
"hard",
"walk"
]
| 23 | 1 | 3 | [
"A000532",
"A001184",
"A003763",
"A007764",
"A120443",
"A121785",
"A121789",
"A145157",
"A271507",
"A363577",
"A384173"
]
| null | Lars Blomberg, Jun 10 2023 | 2025-06-06T08:33:27 | oeisdata/seq/A363/A363577.seq | 45f969f25573f84e961d35cfc09dadec |
A363578 | G.f. satisfies A(x) = exp( Sum_{k>=1} ((-2)^k + A(x^k)) * x^k/k ). | [
"1",
"-1",
"2",
"-2",
"4",
"-6",
"13",
"-20",
"38",
"-65",
"129",
"-228",
"435",
"-794",
"1528",
"-2833",
"5421",
"-10189",
"19561",
"-37091",
"71247",
"-135973",
"261879",
"-502303",
"969181",
"-1866210",
"3608664",
"-6970576",
"13504298",
"-26152744",
"50758711",
"-98515611",
"191517618",
"-372404560",
"725061378"
]
| [
"sign"
]
| 10 | 0 | 3 | [
"A001678",
"A036249",
"A362389",
"A363541",
"A363578",
"A363579",
"A363580"
]
| null | Seiichi Manyama, Jun 10 2023 | 2023-06-10T09:57:30 | oeisdata/seq/A363/A363578.seq | c1334360253a228bbe5cd8b19a0f9137 |
A363579 | G.f. satisfies A(x) = exp( Sum_{k>=1} ((-3)^k + A(x^k)) * x^k/k ). | [
"1",
"-2",
"5",
"-11",
"27",
"-70",
"188",
"-502",
"1355",
"-3712",
"10269",
"-28546",
"79777",
"-224153",
"632581",
"-1791644",
"5091109",
"-14510079",
"41464784",
"-118773034",
"340950420",
"-980660721",
"2825700987",
"-8155455450",
"23573749136",
"-68236663474",
"197774787066",
"-573915774310",
"1667300177595"
]
| [
"sign"
]
| 12 | 0 | 2 | [
"A001678",
"A036249",
"A362389",
"A363541",
"A363578",
"A363579",
"A363581"
]
| null | Seiichi Manyama, Jun 10 2023 | 2023-06-10T11:18:13 | oeisdata/seq/A363/A363579.seq | a0758e60b34e57eec58c67608a426f38 |
A363580 | G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * x^k/(k * (1 + 2*x^k)) ). | [
"1",
"1",
"0",
"2",
"0",
"2",
"1",
"6",
"-2",
"11",
"-1",
"30",
"-21",
"76",
"-60",
"223",
"-245",
"653",
"-817",
"2031",
"-2935",
"6521",
"-10067",
"21455",
"-35425",
"72152",
"-123756",
"246752",
"-436854",
"855852",
"-1546777",
"3001811",
"-5513604",
"10630676",
"-19747742",
"37949424",
"-71115077",
"136415279",
"-257301742",
"493313335"
]
| [
"sign"
]
| 11 | 0 | 4 | [
"A052855",
"A198518",
"A363545",
"A363546",
"A363578",
"A363580",
"A363581"
]
| null | Seiichi Manyama, Jun 10 2023 | 2023-06-10T09:57:25 | oeisdata/seq/A363/A363580.seq | 8a56cc931ad641cf4f101ed5ed9c7014 |
A363581 | G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * x^k/(k * (1 + 3*x^k)) ). | [
"1",
"1",
"-1",
"4",
"-6",
"11",
"-22",
"62",
"-151",
"353",
"-867",
"2261",
"-5861",
"15178",
"-39878",
"106099",
"-283823",
"763248",
"-2065453",
"5621318",
"-15368682",
"42190539",
"-116281176",
"321647511",
"-892617214",
"2484583934",
"-6935203356",
"19408586888",
"-54447145335",
"153084848495"
]
| [
"sign"
]
| 7 | 0 | 4 | [
"A052855",
"A198518",
"A363545",
"A363546",
"A363579",
"A363580",
"A363581"
]
| null | Seiichi Manyama, Jun 10 2023 | 2023-06-10T09:57:22 | oeisdata/seq/A363/A363581.seq | b13dbf98e2d888ab0ad065eae545a45e |
A363582 | Number of admissible mesa sets among Stirling permutations of order n. | [
"1",
"2",
"3",
"6",
"12",
"22",
"44",
"88",
"169",
"338",
"676",
"1322",
"2644",
"5288",
"10433",
"20866",
"41732",
"82736",
"165472",
"330944",
"658012",
"1316024",
"2632048",
"5242778",
"10485556",
"20971112",
"41822049",
"83644098",
"167288196",
"333885702",
"667771404",
"1335542808",
"2667053601",
"5334107202",
"10668214404"
]
| [
"nonn"
]
| 21 | 1 | 2 | [
"A289871",
"A328901",
"A328902",
"A359066",
"A359067",
"A363582"
]
| null | Bridget Tenner, Jun 10 2023 | 2023-06-14T12:12:07 | oeisdata/seq/A363/A363582.seq | f191664114b5d31ed7b97c1b2b2262f9 |
A363583 | Numbers k such that 2*phi(k)+k is a prime, where phi is A000010. | [
"1",
"3",
"5",
"7",
"11",
"13",
"15",
"23",
"33",
"35",
"37",
"43",
"47",
"53",
"61",
"67",
"69",
"71",
"77",
"87",
"95",
"103",
"113",
"119",
"123",
"127",
"133",
"137",
"143",
"159",
"163",
"167",
"177",
"181",
"191",
"193",
"209",
"211",
"217",
"249",
"251",
"257",
"259",
"263",
"267",
"271",
"277",
"293",
"299",
"307",
"313",
"329",
"331",
"335",
"337",
"339"
]
| [
"nonn",
"easy"
]
| 28 | 1 | 2 | [
"A000010",
"A056911",
"A068080",
"A088878",
"A363583"
]
| null | Darío Clavijo, Aug 17 2023 | 2023-09-12T15:51:08 | oeisdata/seq/A363/A363583.seq | 1dfae9c7502b8edf11a51f49b560117d |
A363584 | Lexicographically least sequence of distinct positive integers, subject to the constraint that if 1 <= k <= a(m), then either a(m+k) < a(m) or a(m+k) > 2*a(m). | [
"1",
"3",
"2",
"7",
"15",
"4",
"31",
"63",
"127",
"255",
"5",
"11",
"511",
"1023",
"2047",
"4095",
"6",
"8191",
"16383",
"32767",
"23",
"65535",
"131071",
"8",
"17",
"262143",
"524287",
"1048575",
"2097151",
"4194303",
"8388607",
"16777215",
"9",
"33554431",
"67108863",
"134217727",
"268435455",
"536870911",
"47",
"1073741823",
"2147483647"
]
| [
"nonn"
]
| 23 | 1 | 2 | null | null | Ali Sada, Aug 17 2023 | 2023-08-24T10:26:36 | oeisdata/seq/A363/A363584.seq | c296fcb200c3c2172cfd289f6802bd39 |
A363585 | Least prime p such that p^n + 6 is the product of n distinct primes. | [
"5",
"2",
"23",
"127",
"71",
"353",
"1279",
"3851",
"3049",
"18913",
"47129",
"352073",
"696809"
]
| [
"nonn",
"hard",
"more"
]
| 18 | 1 | 1 | [
"A000961",
"A001221",
"A005117",
"A280005",
"A358656",
"A362957",
"A363585"
]
| null | J.W.L. (Jan) Eerland, Jun 10 2023 | 2024-02-10T05:23:52 | oeisdata/seq/A363/A363585.seq | fa1389afb61ff30ba01b3b26191d65d0 |
A363586 | a(n) is the number of mappings X:{{1..n} choose 3}->{+,-} such that X(a,b,c) = X(b,c,d) implies X(a,b,c) = X(a,b,d) = X(a,c,d) = X(b,c,d) for a < b < c < d. | [
"2",
"10",
"120",
"3284",
"199724",
"26680618",
"7782067930",
"4936744315756"
]
| [
"nonn",
"more"
]
| 28 | 3 | 1 | null | null | Manfred Scheucher, Jun 13 2023 | 2023-06-26T02:07:11 | oeisdata/seq/A363/A363586.seq | e5f9f38b005dad7e2d20b3d944cb467a |
A363587 | Number of partitions of [n] such that in the set of smallest block elements there is an equal number of odd and even terms. | [
"1",
"0",
"1",
"2",
"6",
"16",
"63",
"246",
"1201",
"5632",
"30776",
"166800",
"1032537",
"6404960",
"44200745",
"305485130",
"2305218366",
"17475547664",
"143075155975",
"1179769331662",
"10409877747841",
"92570178170528",
"873953428860952",
"8318955989166944",
"83562716138732321",
"846729015766650672"
]
| [
"nonn"
]
| 16 | 0 | 4 | [
"A000110",
"A290383",
"A363587"
]
| null | Alois P. Heinz, Jun 10 2023 | 2023-11-18T04:02:31 | oeisdata/seq/A363/A363587.seq | 9d478416afd5ea681a5d4f8bbb5b0476 |
A363588 | Number of partitions of [n] having exactly two parity changes within their blocks. | [
"0",
"0",
"0",
"1",
"4",
"17",
"68",
"292",
"1252",
"5670",
"26114",
"126073",
"621914",
"3206277",
"16888898",
"92771126",
"519907322",
"3032369590",
"18012896770",
"111155162265",
"697399200274",
"4537750415991",
"29972920817228",
"204993708306706",
"1421278374189924",
"10188372221843166",
"73948157842293620"
]
| [
"nonn"
]
| 10 | 0 | 5 | [
"A000110",
"A363493",
"A363588"
]
| null | Alois P. Heinz, Jun 10 2023 | 2023-06-10T17:10:42 | oeisdata/seq/A363/A363588.seq | 05af62f16652ce7edaeebd8493ae5c98 |
A363589 | Number of partitions of [2n+1] such that the largest element of each block is odd. | [
"1",
"2",
"8",
"56",
"584",
"8360",
"155720",
"3633704",
"103284296",
"3499082408",
"138860069192",
"6364334129192",
"332934707138888",
"19681714722718376",
"1303617735072968264",
"96028608749005335080",
"7816178772774327523400",
"698943538498179895072424",
"68316963055524325115842376"
]
| [
"nonn"
]
| 13 | 0 | 2 | [
"A000110",
"A290383",
"A307375",
"A363589"
]
| null | Alois P. Heinz, Jun 10 2023 | 2023-06-12T17:22:45 | oeisdata/seq/A363/A363589.seq | 8438da919d4cdea6842e5184f05332c3 |
A363590 | a(n) = Sum_{d|n, d odd} d^d. | [
"1",
"1",
"28",
"1",
"3126",
"28",
"823544",
"1",
"387420517",
"3126",
"285311670612",
"28",
"302875106592254",
"823544",
"437893890380862528",
"1",
"827240261886336764178",
"387420517",
"1978419655660313589123980",
"3126",
"5842587018385982521381947992",
"285311670612"
]
| [
"nonn",
"easy"
]
| 38 | 1 | 3 | [
"A000593",
"A050999",
"A051000",
"A062796",
"A292919",
"A333823",
"A333824",
"A363590",
"A363991"
]
| null | Seiichi Manyama, Jul 08 2023 | 2023-07-26T03:21:51 | oeisdata/seq/A363/A363590.seq | bf25126e9ad66314effd508f7ae836ff |
A363591 | a(n) = 3*(3^(n-1) - 2^n + 1)/2 - binomial(n,2), n >= 3. | [
"0",
"12",
"65",
"255",
"882",
"2870",
"9039",
"27945",
"85448",
"259512",
"784797",
"2366819",
"7125198",
"21424938",
"64373339",
"193316877",
"580344132",
"1741819148",
"5227030665",
"15684238119",
"47059006250",
"141189602142",
"423593972775",
"1270832250545",
"3812597415552",
"11437993573920",
"34314383375669"
]
| [
"nonn",
"easy"
]
| 18 | 3 | 2 | [
"A001117",
"A363591",
"A363603"
]
| null | Enrique Navarrete, Jun 10 2023 | 2024-08-30T10:19:00 | oeisdata/seq/A363/A363591.seq | 62322e13f2b1c16b25da83e76ef65fae |
A363592 | Number of partitions of [n] such that in each block the smallest element has the same parity as the largest element. | [
"1",
"1",
"1",
"3",
"6",
"20",
"55",
"223",
"761",
"3595",
"14532",
"77818",
"361605",
"2155525",
"11274781",
"73822175",
"428004750",
"3046519516",
"19348533739",
"148493347507",
"1023481273549",
"8412534272415",
"62450994058052",
"546699337652602",
"4343869829492281",
"40308548641909593",
"340994681344324137"
]
| [
"nonn"
]
| 14 | 0 | 4 | [
"A000110",
"A131719",
"A361084",
"A363592"
]
| null | Alois P. Heinz, Jun 10 2023 | 2023-06-12T11:35:17 | oeisdata/seq/A363/A363592.seq | 802bfcfbb6045d782e896fa3368f0050 |
A363593 | Numbers k such that both A359804(k) and A359804(k+1) are odd. | [
"3",
"8",
"22",
"29",
"36",
"42",
"45",
"53",
"57",
"64",
"82",
"85",
"88",
"94",
"110",
"119",
"124",
"132",
"135",
"141",
"144",
"152",
"159",
"165",
"170",
"177",
"183",
"190",
"195",
"201",
"214",
"220",
"224",
"231",
"239",
"246",
"252",
"264",
"270",
"281",
"287",
"292",
"299",
"302",
"306",
"309",
"323",
"328",
"334",
"341",
"347",
"350",
"356",
"361",
"372",
"378",
"381",
"386",
"397",
"402",
"411",
"418",
"424",
"431"
]
| [
"nonn"
]
| 17 | 1 | 1 | [
"A000079",
"A053669",
"A100484",
"A359804",
"A361503",
"A361505",
"A363593",
"A363594"
]
| null | Michael De Vlieger and David James Sycamore, Jun 12 2023 | 2023-06-22T06:01:26 | oeisdata/seq/A363/A363593.seq | 1d6c5f02e88f85981cf024f4d523b3c2 |
A363594 | a(n) = the n-th instance of b(k)/2 such that b(k-1) and b(k-2) are both odd, where b(n) = A359804(n). | [
"2",
"4",
"8",
"13",
"16",
"17",
"19",
"23",
"26",
"29",
"31",
"32",
"34",
"37",
"38",
"41",
"43",
"46",
"47",
"53",
"58",
"59",
"61",
"62",
"64",
"67",
"68",
"71",
"73",
"74",
"76",
"79",
"82",
"83",
"86",
"89",
"92",
"94",
"97",
"101",
"103",
"106",
"107",
"109",
"113",
"116",
"118",
"122",
"124",
"127",
"128",
"131",
"134",
"136",
"137",
"139",
"142",
"146",
"148",
"149",
"151",
"152",
"157",
"158",
"163",
"164",
"166",
"167",
"172"
]
| [
"nonn"
]
| 11 | 1 | 1 | [
"A000040",
"A000079",
"A100484",
"A359804",
"A361639",
"A363593",
"A363594"
]
| null | Michael De Vlieger and David James Sycamore, Jun 12 2023 | 2023-07-06T20:56:29 | oeisdata/seq/A363/A363594.seq | 9c2c8668e777bb2700ea0262fa075b03 |
A363595 | Recursive product of aliquot divisors of n. | [
"1",
"1",
"1",
"2",
"1",
"6",
"1",
"16",
"3",
"10",
"1",
"1728",
"1",
"14",
"15",
"2048",
"1",
"5832",
"1",
"8000",
"21",
"22",
"1",
"4586471424",
"5",
"26",
"81",
"21952",
"1",
"24300000",
"1",
"67108864",
"33",
"34",
"35",
"101559956668416",
"1",
"38",
"39",
"163840000000",
"1",
"130691232",
"1",
"85184",
"91125",
"46",
"1",
"16543163447903718821855232",
"7",
"125000",
"51",
"140608",
"1",
"1338925209984"
]
| [
"nonn",
"easy"
]
| 11 | 1 | 4 | [
"A000295",
"A007955",
"A007956",
"A255242",
"A363595"
]
| null | Michael De Vlieger, Jul 10 2023 | 2023-08-02T13:55:44 | oeisdata/seq/A363/A363595.seq | 9b0a912f42218453f19fa39b1cc10a0c |
A363596 | a(n) = (Product_{k=1..pi(n+1)} prime(k)^floor(n/(prime(k)-1) ) )/(n+1)!. | [
"1",
"1",
"2",
"1",
"6",
"2",
"12",
"3",
"10",
"2",
"12",
"2",
"420",
"60",
"24",
"3",
"90",
"10",
"420",
"42",
"660",
"60",
"360",
"30",
"3276",
"252",
"56",
"4",
"120",
"8",
"3696",
"231",
"3570",
"210",
"36",
"2",
"103740",
"5460",
"840",
"42",
"13860",
"660",
"27720",
"1260",
"19320",
"840",
"5040",
"210",
"198900",
"7956",
"10296",
"396",
"11880",
"440",
"6384",
"228"
]
| [
"nonn",
"easy"
]
| 7 | 0 | 3 | [
"A000142",
"A000720",
"A091137",
"A361098",
"A363596"
]
| null | Michael De Vlieger, Aug 03 2023 | 2023-08-05T21:32:50 | oeisdata/seq/A363/A363596.seq | 2cc9e47dd5eb8c5b898eb7ef276b743a |
A363597 | Union of prime powers and numbers that are not squarefree. | [
"1",
"2",
"3",
"4",
"5",
"7",
"8",
"9",
"11",
"12",
"13",
"16",
"17",
"18",
"19",
"20",
"23",
"24",
"25",
"27",
"28",
"29",
"31",
"32",
"36",
"37",
"40",
"41",
"43",
"44",
"45",
"47",
"48",
"49",
"50",
"52",
"53",
"54",
"56",
"59",
"60",
"61",
"63",
"64",
"67",
"68",
"71",
"72",
"73",
"75",
"76",
"79",
"80",
"81",
"83",
"84",
"88",
"89",
"90",
"92",
"96",
"97",
"98",
"99",
"100",
"101",
"103"
]
| [
"nonn",
"easy"
]
| 15 | 1 | 2 | [
"A000040",
"A000961",
"A013929",
"A120944",
"A126706",
"A246547",
"A363597"
]
| null | Michael De Vlieger, Aug 15 2023 | 2024-08-03T01:52:53 | oeisdata/seq/A363/A363597.seq | 865a9f04b2a0976594fb5af27cec922e |
A363598 | Expansion of Sum_{k>0} x^(2*k)/(1+x^k)^4. | [
"0",
"1",
"-4",
"11",
"-20",
"32",
"-56",
"95",
"-124",
"146",
"-220",
"328",
"-364",
"400",
"-584",
"775",
"-816",
"881",
"-1140",
"1486",
"-1600",
"1552",
"-2024",
"2712",
"-2620",
"2562",
"-3400",
"4064",
"-4060",
"4112",
"-4960",
"6231",
"-6208",
"5730",
"-7216",
"8947",
"-8436",
"8000",
"-10248",
"12230",
"-11480",
"11232",
"-13244",
"15752"
]
| [
"sign"
]
| 26 | 1 | 3 | [
"A002129",
"A138503",
"A325940",
"A363022",
"A363598",
"A363604",
"A363613",
"A363614"
]
| null | Seiichi Manyama, Jun 11 2023 | 2023-07-25T17:18:51 | oeisdata/seq/A363/A363598.seq | f542a4af22d4cc5a66761e4004720744 |
A363599 | Number of partitions of n into distinct parts where there are k^2-1 kinds of part k. | [
"1",
"0",
"3",
"8",
"18",
"48",
"109",
"264",
"594",
"1360",
"2988",
"6552",
"14115",
"30048",
"63288",
"131800",
"271953",
"555792",
"1126583",
"2264472",
"4518051",
"8948544",
"17603781",
"34405272",
"66828247",
"129040704",
"247765665",
"473160696",
"898924929",
"1699331808",
"3197083220",
"5987288352",
"11162934948"
]
| [
"nonn",
"easy"
]
| 14 | 0 | 3 | [
"A027998",
"A052812",
"A255835",
"A363599",
"A363600",
"A363601"
]
| null | Seiichi Manyama, Jun 10 2023 | 2023-06-11T11:14:50 | oeisdata/seq/A363/A363599.seq | 51799cc6cc7193a2bcbf724c2e5e013f |
A363600 | Number of partitions of n into distinct parts where there are k^2+1 kinds of part k. | [
"1",
"2",
"6",
"20",
"52",
"140",
"356",
"880",
"2123",
"5016",
"11610",
"26400",
"59130",
"130476",
"284216",
"611592",
"1301344",
"2740194",
"5713930",
"11806144",
"24184908",
"49142504",
"99091244",
"198360536",
"394342884",
"778818658",
"1528531702",
"2982017956",
"5784365082",
"11158728448",
"21413292868"
]
| [
"nonn",
"easy"
]
| 13 | 0 | 2 | [
"A027998",
"A219555",
"A255834",
"A363599",
"A363600",
"A363602"
]
| null | Seiichi Manyama, Jun 10 2023 | 2023-06-11T11:14:55 | oeisdata/seq/A363/A363600.seq | cc89bfc854fd5dcaa9eea79d7c80579b |
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