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2025-04-28 00:58:08
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---|---|---|---|---|---|---|---|---|---|---|---|---|
A382789 | The number of prime factors of Euler phi of the n-th primorial number, counted with multiplicity. | [
"0",
"0",
"1",
"3",
"5",
"7",
"10",
"14",
"17",
"19",
"22",
"25",
"29",
"33",
"36",
"38",
"41",
"43",
"47",
"50",
"53",
"58",
"61",
"63",
"67",
"73",
"77",
"80",
"82",
"87",
"92",
"96",
"99",
"103",
"106",
"109",
"113",
"117",
"122",
"124",
"127",
"129",
"134",
"137",
"144",
"148",
"152",
"156",
"159",
"161",
"165",
"169",
"172",
"178",
"182",
"190",
"192",
"195",
"200",
"204"
] | [
"nonn",
"easy"
] | 7 | 0 | 4 | [
"A000010",
"A001222",
"A002110",
"A023508",
"A055768",
"A055769",
"A382789"
] | null | Amiram Eldar, Apr 05 2025 | 2025-04-05T09:10:10 | oeisdata/seq/A382/A382789.seq | c2566bd13d8e8415785d7f8c45e5b413 |
A382790 | a(n) is the (2^n)-th powerful number. | [
"1",
"4",
"9",
"32",
"121",
"392",
"1352",
"5000",
"18432",
"69192",
"265837",
"1024144",
"3968064",
"15523600",
"60972500",
"240413400",
"950612224",
"3767130288",
"14959246864",
"59495990724",
"236902199076",
"944193944097",
"3765996039168",
"15029799230264",
"60010866324576",
"239700225078125",
"957712290743329"
] | [
"nonn",
"changed"
] | 12 | 0 | 2 | [
"A001694",
"A062762",
"A090699",
"A376092",
"A382790"
] | null | Amiram Eldar, Apr 05 2025 | 2025-04-15T11:58:39 | oeisdata/seq/A382/A382790.seq | 3e4e40a0f973f33aebb016c11beafaf4 |
A382791 | Carmichael numbers with exactly 3 prime factors, p*q*r, such that p-1, q-1 and r-1 have an equal 2-adic valuation. | [
"8911",
"29341",
"314821",
"410041",
"1024651",
"1152271",
"5481451",
"10267951",
"14913991",
"15247621",
"36765901",
"64377991",
"67902031",
"133800661",
"139952671",
"178482151",
"188516329",
"299736181",
"362569201",
"368113411",
"395044651",
"532758241",
"579606301",
"612816751",
"620169409",
"625482001",
"652969351"
] | [
"nonn"
] | 9 | 1 | 1 | [
"A002997",
"A007814",
"A087788",
"A329799",
"A382791"
] | null | Amiram Eldar, Apr 05 2025 | 2025-04-05T09:10:49 | oeisdata/seq/A382/A382791.seq | c5e5a9992dea6c80f2ebd41824957ef4 |
A382792 | a(n) = Sum_{k=0..n} (Stirling1(n,k) * k!)^2. | [
"1",
"1",
"5",
"76",
"2392",
"126676",
"10057204",
"1114096320",
"163918005696",
"30894047577216",
"7254176241285504",
"2075722128162164736",
"710883208780304954112",
"287061726161439955116288",
"134961239570613490548986112",
"73079781978184515947237031936",
"45150931601954398539342470578176"
] | [
"nonn"
] | 16 | 0 | 3 | [
"A006252",
"A007840",
"A047796",
"A048144",
"A379821",
"A382792",
"A382794"
] | null | Ilya Gutkovskiy, Apr 05 2025 | 2025-04-05T16:09:44 | oeisdata/seq/A382/A382792.seq | 5dffef11d84abce61635cc7605d92b92 |
A382793 | a(n) = Sum_{k=0..n} (-1)^k * (Stirling2(n,k) * k!)^2. | [
"1",
"-1",
"3",
"-1",
"-525",
"21599",
"-575757",
"-11712961",
"4147828275",
"-478419026401",
"27474795508083",
"3849481231073279",
"-1772585499434165325",
"366912253456842693599",
"-26525609280231515934477",
"-17189616925094873258825281",
"10414911263566240831226298675",
"-3136992122810471155294591778401"
] | [
"sign"
] | 5 | 0 | 3 | [
"A047797",
"A048144",
"A192552",
"A382793"
] | null | Ilya Gutkovskiy, Apr 05 2025 | 2025-04-05T10:24:32 | oeisdata/seq/A382/A382793.seq | 0f21af10ba94996b5972f2b99cef6df7 |
A382794 | a(n) = Sum_{k=0..n} Stirling1(n,k) * Stirling2(n,k) * (k!)^2. | [
"1",
"1",
"3",
"2",
"-418",
"-14676",
"-234344",
"18565056",
"2659703616",
"169046742960",
"-6539356064736",
"-4061128974843744",
"-672969012637199040",
"-19289566159655581440",
"27323548725052131528960",
"10157639436460221570630144",
"1433264952547826545065237504",
"-520046813680980959472490690560"
] | [
"sign"
] | 6 | 0 | 3 | [
"A000670",
"A006252",
"A047792",
"A048144",
"A064618",
"A192554",
"A192564",
"A382792",
"A382794"
] | null | Ilya Gutkovskiy, Apr 05 2025 | 2025-04-05T10:24:29 | oeisdata/seq/A382/A382794.seq | 69fed55eda2da0ab8bb1875228463953 |
A382795 | Number of minimum total dominating sets in the n-odd graph. | [
"0",
"3",
"10",
"3570",
"52920"
] | [
"nonn",
"more"
] | 4 | 1 | 2 | null | null | Eric W. Weisstein, Apr 05 2025 | 2025-04-05T09:10:01 | oeisdata/seq/A382/A382795.seq | 5ac4cdab73596d3dc82aa5ee5470bc93 |
A382796 | Numbers that can be represented as the sum of two distinct Ulam numbers in more than one way. | [
"5",
"7",
"9",
"10",
"12",
"14",
"15",
"17",
"19",
"20",
"21",
"22",
"24",
"27",
"29",
"30",
"31",
"32",
"34",
"37",
"39",
"40",
"41",
"42",
"44",
"46",
"49",
"50",
"51",
"52",
"54",
"55",
"56",
"58",
"59",
"60",
"61",
"63",
"64",
"65",
"66",
"68",
"70",
"71",
"73",
"74",
"75",
"76",
"78",
"79",
"80",
"81",
"83",
"84",
"85",
"86",
"88",
"89",
"90",
"91",
"93",
"95",
"98",
"100",
"101"
] | [
"nonn"
] | 10 | 1 | 1 | [
"A002858",
"A033629",
"A138892",
"A382796"
] | null | Shyam Sunder Gupta, Apr 05 2025 | 2025-04-06T15:00:52 | oeisdata/seq/A382/A382796.seq | 0b97d060dac370945bfb1d6fe7ca1cb0 |
A382797 | Odd Ulam numbers. | [
"1",
"3",
"11",
"13",
"47",
"53",
"57",
"69",
"77",
"87",
"97",
"99",
"131",
"145",
"155",
"175",
"177",
"189",
"197",
"209",
"219",
"221",
"241",
"243",
"253",
"273",
"309",
"319",
"339",
"341",
"363",
"409",
"429",
"431",
"441",
"451",
"483",
"485",
"497",
"585",
"605",
"607",
"627",
"673",
"685",
"695",
"739",
"751",
"781",
"783",
"847",
"849",
"861",
"891"
] | [
"nonn"
] | 12 | 1 | 2 | [
"A002858",
"A005408",
"A382797"
] | null | Shyam Sunder Gupta, Apr 05 2025 | 2025-04-06T15:01:23 | oeisdata/seq/A382/A382797.seq | 66f6d19c888921d6d23e384c5490621e |
A382798 | Even Ulam numbers. | [
"2",
"4",
"6",
"8",
"16",
"18",
"26",
"28",
"36",
"38",
"48",
"62",
"72",
"82",
"102",
"106",
"114",
"126",
"138",
"148",
"180",
"182",
"206",
"236",
"238",
"258",
"260",
"282",
"316",
"324",
"356",
"358",
"370",
"382",
"390",
"400",
"402",
"412",
"414",
"434",
"456",
"502",
"522",
"524",
"544",
"546",
"566",
"568",
"602",
"612",
"624",
"646",
"668",
"688",
"690"
] | [
"nonn"
] | 11 | 1 | 1 | [
"A002858",
"A005843",
"A382798"
] | null | Shyam Sunder Gupta, Apr 05 2025 | 2025-04-06T15:01:34 | oeisdata/seq/A382/A382798.seq | 1fcd1f711f6ce57ca2d1b04df730908d |
A382799 | Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] 1 / (1 - log(1-x) * log(1-y))^2. | [
"1",
"0",
"0",
"0",
"2",
"0",
"0",
"2",
"2",
"0",
"0",
"4",
"14",
"4",
"0",
"0",
"12",
"40",
"40",
"12",
"0",
"0",
"48",
"144",
"260",
"144",
"48",
"0",
"0",
"240",
"648",
"1284",
"1284",
"648",
"240",
"0",
"0",
"1440",
"3528",
"6936",
"9588",
"6936",
"3528",
"1440",
"0",
"0",
"10080",
"22608",
"42744",
"65928",
"65928",
"42744",
"22608",
"10080",
"0",
"0",
"80640",
"166896",
"300240",
"476808",
"581952",
"476808",
"300240",
"166896",
"80640",
"0"
] | [
"nonn",
"tabl"
] | 12 | 0 | 5 | [
"A379821",
"A382734",
"A382799",
"A382800",
"A382801",
"A382804"
] | null | Seiichi Manyama, Apr 05 2025 | 2025-04-05T16:10:01 | oeisdata/seq/A382/A382799.seq | 546673794533efca1758854f2daa0099 |
A382800 | Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] 1 / (1 - log(1-x) * log(1-y))^3. | [
"1",
"0",
"0",
"0",
"3",
"0",
"0",
"3",
"3",
"0",
"0",
"6",
"27",
"6",
"0",
"0",
"18",
"78",
"78",
"18",
"0",
"0",
"72",
"282",
"588",
"282",
"72",
"0",
"0",
"360",
"1272",
"2988",
"2988",
"1272",
"360",
"0",
"0",
"2160",
"6936",
"16344",
"24612",
"16344",
"6936",
"2160",
"0",
"0",
"15120",
"44496",
"101448",
"175632",
"175632",
"101448",
"44496",
"15120",
"0"
] | [
"nonn",
"tabl"
] | 13 | 0 | 5 | [
"A379821",
"A382735",
"A382799",
"A382800",
"A382802",
"A382806"
] | null | Seiichi Manyama, Apr 05 2025 | 2025-04-05T16:09:57 | oeisdata/seq/A382/A382800.seq | 2323130a644a87822a720f595f1cbab0 |
A382801 | Square array A(n,k), n >= 1, k >= 1, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] (1/2) * (1 / (1 - log(1-x) * log(1-y))^2 - 1). | [
"1",
"1",
"1",
"2",
"7",
"2",
"6",
"20",
"20",
"6",
"24",
"72",
"130",
"72",
"24",
"120",
"324",
"642",
"642",
"324",
"120",
"720",
"1764",
"3468",
"4794",
"3468",
"1764",
"720",
"5040",
"11304",
"21372",
"32964",
"32964",
"21372",
"11304",
"5040",
"40320",
"83448",
"150120",
"238404",
"290976",
"238404",
"150120",
"83448",
"40320"
] | [
"nonn",
"tabl"
] | 14 | 1 | 4 | [
"A382740",
"A382799",
"A382801"
] | null | Seiichi Manyama, Apr 05 2025 | 2025-04-05T23:17:14 | oeisdata/seq/A382/A382801.seq | 011b1d98eb23517f5ae0d41409253c95 |
A382802 | Square array A(n,k), n >= 1, k >= 1, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] (1/3) * (1 / (1 - log(1-x) * log(1-y))^3 - 1). | [
"1",
"1",
"1",
"2",
"9",
"2",
"6",
"26",
"26",
"6",
"24",
"94",
"196",
"94",
"24",
"120",
"424",
"996",
"996",
"424",
"120",
"720",
"2312",
"5448",
"8204",
"5448",
"2312",
"720",
"5040",
"14832",
"33816",
"58544",
"58544",
"33816",
"14832",
"5040",
"40320",
"109584",
"238656",
"431632",
"556376",
"431632",
"238656",
"109584",
"40320"
] | [
"nonn",
"tabl"
] | 16 | 1 | 4 | [
"A382741",
"A382800",
"A382802"
] | null | Seiichi Manyama, Apr 05 2025 | 2025-04-05T23:17:20 | oeisdata/seq/A382/A382802.seq | 6882964a02cc16788fc9d6bd554c5b38 |
A382803 | Positive integers m such that phi(m) and phi(m+1) are both powers of 2. | [
"1",
"2",
"3",
"4",
"5",
"15",
"16",
"255",
"256",
"65535",
"65536",
"4294967295"
] | [
"nonn",
"hard",
"new"
] | 41 | 1 | 2 | [
"A000010",
"A000215",
"A003401",
"A019434",
"A051179",
"A382519",
"A382803"
] | null | Caleb Stanford, Apr 05 2025 | 2025-04-18T21:29:29 | oeisdata/seq/A382/A382803.seq | 4dfdee03cdfe0eea12bafed5d51961a4 |
A382804 | a(n) = Sum_{k=0..n} k! * (k+1)! * Stirling1(n,k)^2. | [
"1",
"2",
"14",
"260",
"9588",
"581952",
"52096512",
"6423520896",
"1041005447424",
"214260350714496",
"54547409318781312",
"16820040059243046144",
"6175245603727007034624",
"2661063379044058584861696",
"1329787781176741647226481664",
"762665713456216694195942866944"
] | [
"nonn"
] | 14 | 0 | 2 | [
"A382737",
"A382792",
"A382799",
"A382804",
"A382806"
] | null | Seiichi Manyama, Apr 05 2025 | 2025-04-05T16:09:35 | oeisdata/seq/A382/A382804.seq | 8720814927f72dfd3a3893d63957b14b |
A382805 | a(n) = Sum_{k=0..n} (-1)^(n-k) * (Stirling1(n,k) * k!)^2. | [
"1",
"1",
"3",
"4",
"-272",
"-8524",
"-96596",
"9634752",
"983055168",
"36429411456",
"-4303305703296",
"-1051644384152064",
"-89651253435644160",
"10632887072757561600",
"5599203549778990667520",
"914684633796830925275136",
"-89559567563652079025946624",
"-104514775371103880549281775616"
] | [
"sign"
] | 4 | 0 | 3 | [
"A006252",
"A007840",
"A047796",
"A048144",
"A192554",
"A320502",
"A382792",
"A382793",
"A382805"
] | null | Ilya Gutkovskiy, Apr 05 2025 | 2025-04-06T14:56:50 | oeisdata/seq/A382/A382805.seq | dc99617f175f826a5f374546bf0b1702 |
A382806 | a(n) = Sum_{k=0..n} (k!)^2 * binomial(k+2,2) * Stirling1(n,k)^2. | [
"1",
"3",
"27",
"588",
"24612",
"1669128",
"165049224",
"22269896064",
"3918921022656",
"870149951146944",
"237662482188210624",
"78249086559726140160",
"30547324837444471084800",
"13946361918619108837939200",
"7359961832428044552536217600",
"4444946383758589481684168540160"
] | [
"nonn"
] | 9 | 0 | 2 | [
"A382738",
"A382792",
"A382800",
"A382804",
"A382806"
] | null | Seiichi Manyama, Apr 05 2025 | 2025-04-05T16:09:31 | oeisdata/seq/A382/A382806.seq | fd4a27d1e0aeb9f3d9652fb57fa5ae9e |
A382807 | a(n) = Sum_{k=0..n} (Stirling1(n,k) * k!)^3. | [
"1",
"1",
"7",
"8",
"-22400",
"-3821176",
"733375592",
"1324952888832",
"521577465629184",
"-1322687167356985344",
"-3493561791052460040192",
"83811280007607865122816",
"33603928402796871413168222208",
"112696506862115060894313558528000",
"-389416384673353674591900391305326592"
] | [
"sign"
] | 5 | 0 | 3 | [
"A006252",
"A242280",
"A382792",
"A382807",
"A382808"
] | null | Ilya Gutkovskiy, Apr 05 2025 | 2025-04-06T14:57:01 | oeisdata/seq/A382/A382807.seq | ec9c4e9f5a7e8ff6799810c8d39198ce |
A382808 | a(n) = Sum_{k=0..n} (|Stirling1(n,k)| * k!)^3. | [
"1",
"1",
"9",
"440",
"71344",
"25826824",
"17321581592",
"19304140340736",
"33142988156751360",
"82906630912116006912",
"289508760665893747703808",
"1364207202603804952193826816",
"8438589244471363680258331914240",
"66972265137135031645961782287814656",
"668922701586813036491303458870218731520"
] | [
"nonn"
] | 7 | 0 | 3 | [
"A007840",
"A242280",
"A382792",
"A382807",
"A382808"
] | null | Ilya Gutkovskiy, Apr 05 2025 | 2025-04-06T05:52:03 | oeisdata/seq/A382/A382808.seq | 445fce080d911cd74b83b87767a6716c |
A382809 | a(n) = (6*n + 1)*(12*n + 1)*(18*n + 1). | [
"1",
"1729",
"12025",
"38665",
"89425",
"172081",
"294409",
"464185",
"689185",
"977185",
"1335961",
"1773289",
"2296945",
"2914705",
"3634345",
"4463641",
"5410369",
"6482305",
"7687225",
"9032905",
"10527121",
"12177649",
"13992265",
"15978745",
"18144865",
"20498401",
"23047129",
"25798825",
"28761265",
"31942225",
"35349481"
] | [
"nonn",
"easy"
] | 12 | 0 | 2 | [
"A002476",
"A002997",
"A016921",
"A017533",
"A033502",
"A046025",
"A068228",
"A161705",
"A382809"
] | null | Stefano Spezia, Apr 05 2025 | 2025-04-06T06:17:50 | oeisdata/seq/A382/A382809.seq | 99b2bf436e34123711b03fee3c133e22 |
A382810 | Primes p such that p + 6, p + 10 and p + 16 are also primes. | [
"7",
"13",
"31",
"37",
"73",
"97",
"157",
"223",
"373",
"433",
"1087",
"1291",
"1423",
"1483",
"1543",
"1861",
"1987",
"2341",
"2383",
"2677",
"2683",
"3313",
"3607",
"4441",
"4507",
"4783",
"4993",
"5641",
"5851",
"6037",
"6961",
"7237",
"7867",
"8731",
"9613",
"9733",
"10723",
"13093",
"13681",
"14143",
"14731",
"16057",
"16411",
"16921",
"17377"
] | [
"nonn",
"changed"
] | 18 | 1 | 1 | [
"A000040",
"A001223",
"A023200",
"A031924",
"A033451",
"A078852",
"A078856",
"A078858",
"A382810"
] | null | Alexander Yutkin, Apr 05 2025 | 2025-04-25T15:14:29 | oeisdata/seq/A382/A382810.seq | 5583920ef139b00af4da4523bcf387e0 |
A382811 | Integers k such that d*2^k - 1 is prime for some divisor d of k. | [
"2",
"3",
"4",
"5",
"6",
"7",
"10",
"12",
"13",
"16",
"17",
"18",
"19",
"21",
"28",
"30",
"31",
"36",
"42",
"46",
"54",
"60",
"61",
"63",
"75",
"81",
"88",
"89",
"99",
"102",
"104",
"106",
"107",
"108",
"115",
"123",
"126",
"127",
"132",
"133",
"204",
"214",
"216",
"225",
"249",
"264",
"270",
"286",
"304",
"306",
"324",
"330",
"342",
"352",
"362",
"384",
"390"
] | [
"nonn",
"new"
] | 40 | 1 | 1 | [
"A000043",
"A002234",
"A382811"
] | null | Juri-Stepan Gerasimov, Apr 15 2025 | 2025-04-25T15:56:15 | oeisdata/seq/A382/A382811.seq | 9620fdfebf0db627acb00962fb38a264 |
A382812 | Numerator of the n-th partial sum of the squares of the harmonic numbers. | [
"1",
"13",
"119",
"1577",
"3233",
"8867",
"141563",
"2844129",
"28119709",
"335676251",
"3968696491",
"55023970333",
"758025067309",
"799020611041",
"1676892996083",
"59597395635137",
"351844709221043",
"2314823924364859",
"9114392136427625",
"628176680098075",
"216039223801697",
"5117413095318143",
"363066107054194281",
"27957386425926920257"
] | [
"nonn",
"frac",
"changed"
] | 33 | 1 | 2 | [
"A001008",
"A002805",
"A027611",
"A027612",
"A382812",
"A382813"
] | null | Gary Detlefs, Apr 05 2025 | 2025-04-25T17:15:55 | oeisdata/seq/A382/A382812.seq | a8b49701b29af538f17cf35d4fd0262d |
A382813 | Denominator of the n-th partial sum of the squares of the harmonic numbers. | [
"1",
"4",
"18",
"144",
"200",
"400",
"4900",
"78400",
"635040",
"6350400",
"64033200",
"768398400",
"9275666400",
"8657288640",
"16232416200",
"519437318400",
"2779951574400",
"16679709446400",
"60213751101504",
"3823095308032",
"1216439416192",
"26761667156224",
"1769615240705312",
"127412297330782464",
"3062795608913040000"
] | [
"nonn",
"frac",
"changed"
] | 29 | 1 | 2 | [
"A001008",
"A002805",
"A027611",
"A027612",
"A382812",
"A382813"
] | null | Gary Detlefs, Apr 05 2025 | 2025-04-25T17:15:32 | oeisdata/seq/A382/A382813.seq | 7daf1e47786f577e3dfc666ad01bfad6 |
A382814 | Number of nachos that the first player gets when playing the "Fibonachos" game starting with n nachos. | [
"1",
"1",
"2",
"3",
"3",
"4",
"3",
"4",
"4",
"5",
"6",
"8",
"8",
"9",
"9",
"9",
"10",
"10",
"12",
"8",
"9",
"9",
"10",
"11",
"11",
"12",
"11",
"12",
"12",
"13",
"14",
"16",
"21",
"21",
"22",
"22",
"22",
"23",
"23",
"25",
"25",
"26",
"26",
"26",
"25",
"26",
"26",
"27",
"28",
"28",
"29",
"28",
"33",
"21",
"22",
"22",
"23",
"24",
"24",
"25",
"24",
"25",
"25",
"26",
"27",
"29",
"29",
"30",
"30",
"30"
] | [
"nonn"
] | 10 | 1 | 3 | [
"A000045",
"A280521",
"A382814"
] | null | Peter Kagey, Apr 05 2025 | 2025-04-12T12:38:46 | oeisdata/seq/A382/A382814.seq | c5af6fe02fde0ade8bc0eb903b4aaf2a |
A382816 | a(n) = number of occurrences of n in A008949. | [
"1",
"1",
"2",
"1",
"1",
"2",
"2",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"3",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"2",
"1",
"2",
"2",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"1",
"1",
"1",
"2",
"3",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1"
] | [
"nonn"
] | 13 | 2 | 3 | [
"A007318",
"A008949",
"A382816",
"A382817"
] | null | Clark Kimberling, Apr 07 2025 | 2025-04-13T11:47:20 | oeisdata/seq/A382/A382816.seq | 036378d16591fd1757c4435100853370 |
A382817 | a(n) = number of primes among the partial sums of row n of Pascal's triangle (A007318). | [
"0",
"1",
"1",
"1",
"2",
"1",
"1",
"2",
"2",
"0",
"2",
"1",
"3",
"2",
"3",
"2",
"3",
"1",
"1",
"2",
"1",
"1",
"2",
"2",
"1",
"1",
"2",
"3",
"3",
"0",
"2",
"7",
"2",
"0",
"0",
"1",
"1",
"0",
"0",
"0",
"2",
"0",
"1",
"1",
"1",
"0",
"1",
"3",
"1",
"0",
"1",
"1",
"1",
"1",
"1",
"1",
"5",
"3",
"3",
"2",
"3",
"2",
"3",
"3",
"10",
"0",
"1",
"0",
"1",
"0",
"2",
"2",
"2",
"0",
"0",
"1",
"1",
"0",
"2",
"1",
"1",
"1",
"2",
"1",
"2",
"0"
] | [
"nonn"
] | 21 | 0 | 5 | [
"A007318",
"A008949",
"A258483",
"A382816",
"A382817"
] | null | Clark Kimberling, Apr 07 2025 | 2025-04-13T11:49:16 | oeisdata/seq/A382/A382817.seq | 7b7baacec76265792616d52f249fad5b |
A382818 | Square array A(n,k), n > 0, k > 0, read by downward antidiagonals: A(n,k) is the number of columns in all k-compositions of n. | [
"1",
"2",
"3",
"3",
"11",
"8",
"4",
"24",
"52",
"20",
"5",
"42",
"163",
"227",
"48",
"6",
"65",
"372",
"1017",
"944",
"112",
"7",
"93",
"710",
"3019",
"6030",
"3800",
"256",
"8",
"126",
"1208",
"7095",
"23256",
"34563",
"14944",
"576",
"9",
"164",
"1897",
"14340",
"67251",
"173076",
"193392",
"57748",
"1280",
"10",
"207",
"2808",
"26082",
"161394",
"615630",
"1256936",
"1062756",
"220128",
"2816"
] | [
"nonn",
"easy",
"tabl"
] | 14 | 1 | 2 | [
"A001792",
"A005475",
"A145839",
"A181289",
"A181290",
"A382818",
"A382820"
] | null | John Tyler Rascoe, Apr 05 2025 | 2025-04-06T08:45:19 | oeisdata/seq/A382/A382818.seq | ae59a6f833a7515c215075ca308291a1 |
A382819 | Number of Grassmannian permutations on [n] of order dividing 3. | [
"1",
"1",
"1",
"3",
"5",
"7",
"12",
"17",
"22",
"31",
"40",
"49",
"63",
"77",
"91",
"111",
"131",
"151",
"178",
"205",
"232",
"267",
"302",
"337",
"381",
"425",
"469",
"523",
"577",
"631",
"696",
"761",
"826",
"903",
"980",
"1057",
"1147",
"1237",
"1327",
"1431",
"1535",
"1639",
"1758",
"1877",
"1996",
"2131",
"2266",
"2401",
"2553",
"2705",
"2857",
"3027",
"3197",
"3367",
"3556",
"3745",
"3934"
] | [
"nonn",
"easy"
] | 24 | 0 | 4 | [
"A000325",
"A001470",
"A382819"
] | null | Aaron Geary, Apr 05 2025 | 2025-04-12T16:29:04 | oeisdata/seq/A382/A382819.seq | e964c2131e6a311c7dba36dba733743a |
A382820 | Number of columns in all n-compositions of n. | [
"1",
"11",
"163",
"3019",
"67251",
"1753877",
"52468711",
"1772042699",
"66708748963",
"2770212058261",
"125812351808551",
"6203908746628501",
"330108021642012407",
"18853083403505443593",
"1150352428059538611663",
"74685045367715777653195",
"5140745255774277374241411",
"373950591013899715795929605"
] | [
"nonn",
"easy"
] | 7 | 1 | 2 | [
"A001792",
"A145839",
"A181289",
"A181290",
"A382818",
"A382820"
] | null | John Tyler Rascoe, Apr 05 2025 | 2025-04-06T08:45:09 | oeisdata/seq/A382/A382820.seq | 2dab59feb7a46c1f91d45673e3a46952 |
A382821 | Decimal expansion of (3/2) * (log(3) - 1). | [
"1",
"4",
"7",
"9",
"1",
"8",
"4",
"3",
"3",
"0",
"0",
"2",
"1",
"6",
"4",
"5",
"3",
"7",
"0",
"9",
"2",
"8",
"6",
"7",
"8",
"5",
"5",
"3",
"8",
"3",
"7",
"8",
"8",
"5",
"5",
"6",
"9",
"7",
"1",
"2",
"3",
"5",
"8",
"3",
"6",
"7",
"3",
"4",
"1",
"2",
"4",
"1",
"7",
"7",
"6",
"0",
"2",
"0",
"4",
"1",
"5",
"0",
"0",
"4",
"5",
"6",
"2",
"4",
"1",
"4",
"3",
"9",
"8",
"2",
"7",
"9",
"1",
"3",
"4",
"5",
"0",
"3",
"1",
"0",
"4",
"2",
"3"
] | [
"nonn",
"cons"
] | 13 | 0 | 2 | [
"A016627",
"A016631",
"A093064",
"A145425",
"A382821"
] | null | Sean A. Irvine, Apr 05 2025 | 2025-04-08T04:47:03 | oeisdata/seq/A382/A382821.seq | f5b89bed3fe4b635598240472a271470 |
A382822 | If a(n-1) is odd, then a(n) is the smallest even integer not yet in the sequence; if a(n-1) is even, then a(n) = a(n-1)/2 if this number is not in the sequence, otherwise a(n) = 3*a(n-1)/2; a(1)=1. | [
"1",
"2",
"3",
"4",
"6",
"9",
"8",
"12",
"18",
"27",
"10",
"5",
"14",
"7",
"16",
"24",
"36",
"54",
"81",
"20",
"30",
"15",
"22",
"11",
"26",
"13",
"28",
"42",
"21",
"32",
"48",
"72",
"108",
"162",
"243",
"34",
"17",
"38",
"19",
"40",
"60",
"90",
"45",
"44",
"66",
"33",
"46",
"23",
"50",
"25",
"52",
"78",
"39",
"56",
"84",
"126",
"63",
"58",
"29",
"62",
"31",
"64",
"96",
"144",
"216",
"324",
"486",
"729",
"68",
"102",
"51",
"70",
"35",
"74",
"37",
"76",
"114",
"57"
] | [
"nonn",
"new"
] | 30 | 1 | 2 | [
"A350877",
"A382822"
] | null | Enrique Navarrete, Apr 15 2025 | 2025-04-23T10:21:41 | oeisdata/seq/A382/A382822.seq | 0d358682cbc6fa89e3797450984d3444 |
A382823 | Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] 1 / ( (1-x) * (1-y) * (1 - log(1-x) * log(1-y)) ). | [
"1",
"1",
"1",
"2",
"2",
"2",
"6",
"5",
"5",
"6",
"24",
"17",
"17",
"17",
"24",
"120",
"74",
"69",
"69",
"74",
"120",
"720",
"394",
"338",
"337",
"338",
"394",
"720",
"5040",
"2484",
"1962",
"1894",
"1894",
"1962",
"2484",
"5040",
"40320",
"18108",
"13228",
"12194",
"12152",
"12194",
"13228",
"18108",
"40320",
"362880",
"149904",
"101812",
"89160",
"87320",
"87320",
"89160",
"101812",
"149904",
"362880"
] | [
"nonn",
"tabl"
] | 17 | 0 | 4 | [
"A000142",
"A000774",
"A099594",
"A379821",
"A382823",
"A382824",
"A382825",
"A382826"
] | null | Seiichi Manyama, Apr 05 2025 | 2025-04-06T03:48:25 | oeisdata/seq/A382/A382823.seq | a146359be84965d8c800a0ae263a2525 |
A382824 | Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] 1 / ( (1-x) * (1-y) * (1 - log(1-x) * log(1-y))^2 ). | [
"1",
"1",
"1",
"2",
"3",
"2",
"6",
"8",
"8",
"6",
"24",
"28",
"34",
"28",
"24",
"120",
"124",
"150",
"150",
"124",
"120",
"720",
"668",
"768",
"854",
"768",
"668",
"720",
"5040",
"4248",
"4584",
"5204",
"5204",
"4584",
"4248",
"5040",
"40320",
"31176",
"31512",
"35188",
"37556",
"35188",
"31512",
"31176",
"40320",
"362880",
"259488",
"246072",
"265896",
"290380",
"290380",
"265896",
"246072",
"259488",
"362880"
] | [
"nonn",
"tabl"
] | 12 | 0 | 4 | [
"A382823",
"A382824",
"A382825",
"A382827"
] | null | Seiichi Manyama, Apr 05 2025 | 2025-04-06T08:46:34 | oeisdata/seq/A382/A382824.seq | 27cda19c4822be4fe48e563a0e29d8b1 |
A382825 | Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = n! * k! * [x^n * y^k] 1 / ( (1-x) * (1-y) * (1 - log(1-x) * log(1-y))^3 ). | [
"1",
"1",
"1",
"2",
"4",
"2",
"6",
"11",
"11",
"6",
"24",
"39",
"55",
"39",
"24",
"120",
"174",
"255",
"255",
"174",
"120",
"720",
"942",
"1338",
"1623",
"1338",
"942",
"720",
"5040",
"6012",
"8106",
"10434",
"10434",
"8106",
"6012",
"5040",
"40320",
"44244",
"56292",
"72762",
"82116",
"72762",
"56292",
"44244",
"40320",
"362880",
"369072",
"442860",
"560988",
"668580",
"668580",
"560988",
"442860",
"369072",
"362880"
] | [
"nonn",
"tabl"
] | 11 | 0 | 4 | [
"A382673",
"A382800",
"A382823",
"A382824",
"A382825",
"A382828"
] | null | Seiichi Manyama, Apr 06 2025 | 2025-04-06T08:46:30 | oeisdata/seq/A382/A382825.seq | b93426ccc1644cbd983ecbcd8659bf7f |
A382826 | a(n) = Sum_{k=0..n} (k! * Stirling1(n+1,k+1))^2. | [
"1",
"2",
"17",
"337",
"12152",
"696076",
"58136500",
"6673107316",
"1008077743552",
"193915431216576",
"46281189562936704",
"13420575661095930240",
"4647502230640182602496",
"1894412230202331489632256",
"897850527136410029486517504",
"489578762044356075253626875136"
] | [
"nonn"
] | 10 | 0 | 2 | [
"A048163",
"A382792",
"A382823",
"A382826"
] | null | Seiichi Manyama, Apr 06 2025 | 2025-04-06T05:07:30 | oeisdata/seq/A382/A382826.seq | fee619a1d77b57ff255875b335179ee2 |
A382827 | a(n) = Sum_{k=0..n} k! * (k+1)! * Stirling1(n+1,k+1)^2. | [
"1",
"3",
"34",
"854",
"37556",
"2546852",
"246113904",
"32104625520",
"5433891955968",
"1157778241057152",
"303197684900579712",
"95717977509042032256",
"35847800701044816248064",
"15713483696924130220098816",
"7969364997624587289470810112",
"4630203661005094483980386924544"
] | [
"nonn"
] | 8 | 0 | 2 | [
"A092552",
"A382804",
"A382824",
"A382827"
] | null | Seiichi Manyama, Apr 06 2025 | 2025-04-06T05:08:54 | oeisdata/seq/A382/A382827.seq | b152cfd4ac3f1b08c18e3bbc23bfcb5b |
A382828 | a(n) = Sum_{k=0..n} (k!)^2 * binomial(k+2,2) * Stirling1(n+1,k+1)^2. | [
"1",
"4",
"55",
"1623",
"82116",
"6302028",
"680105112",
"98011315608",
"18163969766592",
"4205977241171328",
"1189459906531372224",
"403300593144673493184",
"161454763431242385682176",
"75337361633768810384542464",
"40524573487904551618353921024",
"24890567631479746511661428751360"
] | [
"nonn"
] | 10 | 0 | 2 | [
"A382676",
"A382806",
"A382825",
"A382828"
] | null | Seiichi Manyama, Apr 06 2025 | 2025-04-06T05:06:06 | oeisdata/seq/A382/A382828.seq | 1b743e427e9d5646a4671fbf99392b1b |
A382829 | Number of distinct rank vectors of distributive lattices of height n. | [
"1",
"1",
"2",
"5",
"15",
"51",
"197",
"864",
"4325",
"24922"
] | [
"nonn",
"more"
] | 5 | 0 | 3 | [
"A000112",
"A006982",
"A382829"
] | null | Ludovic Schwob, Apr 06 2025 | 2025-04-12T12:00:06 | oeisdata/seq/A382/A382829.seq | 74c0b1f432522bad7631cde4d4bb8f39 |
A382830 | a(n) = Sum_{k=0..n} binomial(n+k-1,k) * |Stirling1(n,k)| * k!. | [
"1",
"1",
"8",
"102",
"1804",
"40890",
"1131108",
"36948240",
"1391945616",
"59411849040",
"2833582748160",
"149347596487056",
"8620256620495584",
"540775669746661440",
"36636074309252234880",
"2665704585421541790720",
"207329122282259073044736",
"17165075378189396045777280",
"1507206260097615729874083840"
] | [
"nonn"
] | 6 | 0 | 3 | [
"A007840",
"A052801",
"A277759",
"A305919",
"A354122",
"A354123",
"A382830"
] | null | Ilya Gutkovskiy, Apr 06 2025 | 2025-04-06T14:57:13 | oeisdata/seq/A382/A382830.seq | e3bb07dee0c45e068b59d0fb4ca44d10 |
A382831 | Achilles numbers such that the three numbers before it and the three numbers after it are squarefree. | [
"108",
"392",
"432",
"500",
"968",
"1800",
"1944",
"2592",
"2700",
"3200",
"3456",
"4000",
"4500",
"5400",
"8712",
"8788",
"9000",
"10368",
"10584",
"10800",
"13068",
"13500",
"14112",
"14792",
"16200",
"18000",
"18432",
"20808",
"21168",
"21600",
"21632",
"24696",
"25088",
"25992",
"26136",
"27436",
"31104",
"33800",
"34992",
"37044",
"38088",
"38988"
] | [
"nonn"
] | 10 | 1 | 1 | [
"A005117",
"A052486",
"A068088",
"A373689",
"A382831"
] | null | Massimo Kofler, Apr 06 2025 | 2025-04-12T11:58:47 | oeisdata/seq/A382/A382831.seq | 1817652096999cc5e9b97b95997a0a91 |
A382832 | Least k such that there exist two distinct subsets of {0, ..., k-1} with the same sum of m-th powers for 0 <= m <= n. | [
"2",
"4",
"7",
"12",
"16",
"23",
"31"
] | [
"nonn",
"hard",
"more"
] | 9 | 0 | 1 | [
"A382382",
"A382832",
"A382833"
] | null | Pontus von Brömssen, Apr 10 2025 | 2025-04-12T09:42:45 | oeisdata/seq/A382/A382832.seq | a7a1687f487320cbbfc335b478e6a365 |
A382833 | Square array read by antidiagonals: T(n,k) is the number of distinct sum-of-powers vectors (Sum_{x in X} x^m, 0 <= m <= k) for subsets X of {0, ..., n-1}; n, k >= 0. | [
"1",
"1",
"2",
"1",
"2",
"3",
"1",
"2",
"4",
"4",
"1",
"2",
"4",
"8",
"5",
"1",
"2",
"4",
"8",
"15",
"6",
"1",
"2",
"4",
"8",
"16",
"26",
"7",
"1",
"2",
"4",
"8",
"16",
"32",
"42",
"8",
"1",
"2",
"4",
"8",
"16",
"32",
"64",
"64",
"9",
"1",
"2",
"4",
"8",
"16",
"32",
"64",
"126",
"93",
"10",
"1",
"2",
"4",
"8",
"16",
"32",
"64",
"128",
"247",
"130",
"11",
"1",
"2",
"4",
"8",
"16",
"32",
"64",
"128",
"256",
"476",
"176",
"12"
] | [
"nonn",
"tabl"
] | 4 | 0 | 3 | [
"A000027",
"A000125",
"A382383",
"A382832",
"A382833"
] | null | Pontus von Brömssen, Apr 10 2025 | 2025-04-12T12:46:57 | oeisdata/seq/A382/A382833.seq | 208fb592c0089bb4c7f9746bab2fe955 |
A382834 | Smallest number k > P(n) - prime(n+1)^2 which is coprime to P(n), where P(n)= A002110(n) are the primorials. | [
"-5",
"-17",
"-17",
"97",
"2143",
"29747",
"510151",
"9699167",
"223092031",
"6469692277",
"200560488763",
"7420738133141",
"304250263525363",
"13082761331667823",
"614889782588488607",
"32589158477190041261",
"1922760350154212635351",
"117288381359406970978787",
"7858321551080267055874051"
] | [
"sign",
"easy",
"new"
] | 53 | 1 | 1 | [
"A002110",
"A034386",
"A054270",
"A064819",
"A382834"
] | null | Jakub Buczak, Apr 06 2025 | 2025-04-17T19:25:09 | oeisdata/seq/A382/A382834.seq | 94e4fd99fafadfba6600b88850937b43 |
A382835 | Array read by ascending antidiagonals: A(n,k) = (6*n + 1)*(12*n + 1)*Product_{i=0..k-2} (9*2^i*n + 1) with k >= 2. | [
"1",
"91",
"1",
"325",
"1729",
"1",
"703",
"12025",
"63973",
"1",
"1225",
"38665",
"877825",
"4670029",
"1",
"1891",
"89425",
"4214485",
"127284625",
"677154205",
"1",
"2701",
"172081",
"12966625",
"914543245",
"36785256625",
"195697565245",
"1",
"3655",
"294409",
"31146661",
"3747354625",
"395997225085",
"21225093072625",
"112917495146365",
"1"
] | [
"nonn",
"tabl"
] | 11 | 0 | 2 | [
"A000012",
"A002997",
"A318646",
"A382809",
"A382835",
"A382836"
] | null | Stefano Spezia, Apr 06 2025 | 2025-04-12T12:31:25 | oeisdata/seq/A382/A382835.seq | ef6fb8a61b4e4bb261e1e47476d93a47 |
A382836 | Antidiagonal sums of A382835. | [
"1",
"92",
"2055",
"76702",
"5587745",
"808744632",
"233410506523",
"134542364243426",
"155011115348112933",
"357100810407398252476",
"1645189596276664815781823",
"15158968746195230959317963654",
"279359806252976896009489630292137",
"10296791416488914892304807658835547904",
"759072247447684071473777552807296660596387"
] | [
"nonn"
] | 6 | 0 | 2 | [
"A382835",
"A382836"
] | null | Stefano Spezia, Apr 06 2025 | 2025-04-12T12:31:33 | oeisdata/seq/A382/A382836.seq | 8493cc289f97e0d60122f4547e2a5017 |
A382837 | Numbers k such that k - A071324(k) > A000010(k). | [
"60",
"70",
"84",
"120",
"140",
"154",
"168",
"180",
"200",
"210",
"220",
"240",
"252",
"260",
"264",
"280",
"286",
"300",
"312",
"336",
"340",
"350",
"360",
"374",
"390",
"396",
"408",
"418",
"420",
"442",
"456",
"468",
"480",
"490",
"494",
"504",
"510",
"520",
"528",
"540",
"560",
"570",
"588",
"598",
"600",
"624",
"630",
"646",
"660",
"672",
"680",
"700"
] | [
"nonn"
] | 34 | 1 | 1 | [
"A000010",
"A071324",
"A382837"
] | null | Shreyansh Jaiswal, Apr 06 2025 | 2025-04-13T16:26:46 | oeisdata/seq/A382/A382837.seq | dbee8c1175e0f737dfe8e438d1a9e0fe |
A382838 | a(n) is the least k such that there are exactly n solutions in positive integers to the equation x^3 + y^2 = k^2. | [
"1",
"3",
"15",
"105",
"665",
"1155",
"9240",
"68265",
"200640",
"54285",
"434280",
"3474240",
"19120920",
"1430715",
"451605",
"38629305",
"3612840",
"28902720",
"97546680",
"154900515",
"451605000",
"1239204120",
"2633760360",
"12193335000",
"21070082880",
"28902720000"
] | [
"nonn",
"more"
] | 14 | 0 | 2 | [
"A382338",
"A382838"
] | null | Robert Israel, Apr 06 2025 | 2025-04-12T12:19:33 | oeisdata/seq/A382/A382838.seq | 8d3bec47a6bf3ff58ef817d007cdd6ed |
A382839 | Number of dense binary relations on {1,...,n}. | [
"1",
"2",
"7",
"114",
"9602",
"3962940",
"7516789560",
"62622777447552"
] | [
"nonn",
"more"
] | 20 | 0 | 2 | [
"A382693",
"A382839"
] | null | Mark Bowron, Apr 06 2025 | 2025-04-13T19:02:35 | oeisdata/seq/A382/A382839.seq | d55163527ad416651c023b8d8123ac50 |
A382840 | a(n) = Sum_{k=0..n} binomial(n+k-1,k) * Stirling1(n,k) * k!. | [
"1",
"1",
"4",
"30",
"316",
"4290",
"71268",
"1400112",
"31750416",
"816215760",
"23455342560",
"745073660496",
"25924233481056",
"980518650296640",
"40054724743501440",
"1757539560656401920",
"82439565962427760896",
"4116529729771939393920",
"218017561353648160158720",
"12206586491422209675532800"
] | [
"nonn"
] | 6 | 0 | 3 | [
"A006252",
"A305919",
"A308565",
"A317280",
"A354120",
"A354121",
"A382830",
"A382840"
] | null | Ilya Gutkovskiy, Apr 06 2025 | 2025-04-10T03:25:44 | oeisdata/seq/A382/A382840.seq | e385612abf954961a31ce2eb5fa97357 |
A382841 | a(n) = Sum_{k=0..floor(n/2)} (binomial(n,k) * binomial(n-k,k))^2. | [
"1",
"1",
"5",
"37",
"181",
"1301",
"9401",
"65465",
"498037",
"3796021",
"29221705",
"230396585",
"1828448425",
"14651160265",
"118544522045",
"965075143037",
"7907605360757",
"65162569952245",
"539515760866889",
"4486877961224297",
"37463151704756281",
"313909383754331801",
"2638892573249746445",
"22249830926517611917"
] | [
"nonn",
"changed"
] | 15 | 0 | 3 | [
"A000984",
"A002426",
"A005259",
"A005260",
"A051286",
"A089627",
"A181546",
"A275027",
"A277247",
"A382841",
"A382842"
] | null | Ilya Gutkovskiy, Apr 06 2025 | 2025-04-15T15:10:08 | oeisdata/seq/A382/A382841.seq | a6aac9e2f8b7519fab0602e0abe59255 |
A382842 | a(n) = Sum_{k=0..floor(n/2)} (binomial(n,k) * binomial(n-k,k))^3. | [
"1",
"1",
"9",
"217",
"1945",
"35001",
"764001",
"12079089",
"250222617",
"5424133465",
"107360983009",
"2358751625649",
"52540471866961",
"1147794435985393",
"26151265459123065",
"600227875293254217",
"13779170435209475097",
"322302377797126709913",
"7582484532013652243169",
"179184911648568670363185",
"4275721755296040840336945"
] | [
"nonn"
] | 11 | 0 | 3 | [
"A000172",
"A002426",
"A069865",
"A089627",
"A092813",
"A181545",
"A382841",
"A382842"
] | null | Ilya Gutkovskiy, Apr 06 2025 | 2025-04-09T05:05:52 | oeisdata/seq/A382/A382842.seq | d8de80ffb5e764be0fb106e72a70eb45 |
A382843 | Table read by rows: row n is the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = A000045(n) and its long leg and hypotenuse are consecutive natural numbers. | [
"-1",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"3",
"4",
"5",
"5",
"12",
"13",
"9",
"40",
"41",
"15",
"112",
"113",
"25",
"312",
"313",
"41",
"840",
"841",
"67",
"2244",
"2245",
"109",
"5940",
"5941",
"177",
"15664",
"15665",
"287",
"41184",
"41185",
"465",
"108112",
"108113",
"753",
"283504",
"283505",
"1219",
"742980",
"742981",
"1973",
"1946364",
"1946365",
"3193",
"5097624",
"5097625",
"5167",
"13348944",
"13348945"
] | [
"sign",
"easy",
"tabf"
] | 16 | 0 | 10 | [
"A000045",
"A001595",
"A095122",
"A382843",
"A382844",
"A382845"
] | null | Miguel-Ángel Pérez García-Ortega, Apr 06 2025 | 2025-04-13T16:12:33 | oeisdata/seq/A382/A382843.seq | b6302773672b9614cdcfc664e6e01434 |
A382844 | Area of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = A000045(n) and its long leg and hypotenuse are consecutive natural numbers. | [
"0",
"0",
"0",
"6",
"30",
"180",
"840",
"3900",
"17220",
"75174",
"323730",
"1386264",
"5909904",
"25136040",
"106739256",
"452846310",
"1920088086",
"8138356716",
"34486996824",
"146121685380",
"619066205340",
"2622628707270",
"11110214972010",
"47065148576496",
"199375154768160",
"844577145104400",
"3577713520710960"
] | [
"nonn",
"easy"
] | 12 | 0 | 4 | [
"A000045",
"A095122",
"A382843",
"A382844",
"A382845"
] | null | Miguel-Ángel Pérez García-Ortega, Apr 06 2025 | 2025-04-13T16:12:15 | oeisdata/seq/A382/A382844.seq | 808021e63348f6528f1bf72438c08bac |
A382845 | Sum of the legs of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = A000045(n) and its long leg and hypotenuse are consecutive natural numbers. | [
"-1",
"1",
"1",
"7",
"17",
"49",
"127",
"337",
"881",
"2311",
"6049",
"15841",
"41471",
"108577",
"284257",
"744199",
"1948337",
"5100817",
"13354111",
"34961521",
"91530449",
"239629831",
"627359041",
"1642447297",
"4299982847",
"11257501249",
"29472520897",
"77160061447",
"202007663441",
"528862928881",
"1384581123199"
] | [
"sign",
"easy"
] | 11 | 0 | 4 | [
"A000045",
"A007598",
"A080097",
"A095122",
"A382843",
"A382844",
"A382845"
] | null | Miguel-Ángel Pérez García-Ortega, Apr 06 2025 | 2025-04-13T16:11:56 | oeisdata/seq/A382/A382845.seq | ceca6d31a08aaf94e29de71cc17875b3 |
A382846 | Decimal expansion of 4 - Pi^2/4 - 2*log(2). | [
"1",
"4",
"6",
"3",
"0",
"4",
"5",
"3",
"8",
"6",
"0",
"7",
"7",
"6",
"9",
"7",
"2",
"6",
"4",
"5",
"6",
"9",
"1",
"3",
"0",
"0",
"7",
"1",
"1",
"4",
"6",
"0",
"9",
"0",
"8",
"0",
"0",
"2",
"0",
"5",
"7",
"4",
"8",
"7",
"9",
"4",
"6",
"9",
"2",
"9",
"1",
"8",
"3",
"5",
"1",
"5",
"5",
"3",
"0",
"2",
"6",
"3",
"6",
"9",
"5",
"8",
"2",
"0",
"1",
"5",
"5",
"0",
"4",
"5",
"5",
"8",
"0",
"9",
"2",
"5",
"8",
"0",
"3",
"7",
"8",
"2",
"9"
] | [
"nonn",
"cons"
] | 5 | 0 | 2 | [
"A016627",
"A091476",
"A382846"
] | null | Sean A. Irvine, Apr 06 2025 | 2025-04-06T16:51:23 | oeisdata/seq/A382/A382846.seq | 8beb986e50acb4e9d72d4f9f71f547dc |
A382847 | a(n) = Sum_{k=0..n} binomial(n+k-1,k) * (Stirling2(n,k) * k!)^2. | [
"1",
"1",
"14",
"579",
"48044",
"6647405",
"1379024730",
"400315753159",
"154879704709784",
"77018569697097009",
"47863427797633958630",
"36348262891572161261963",
"33119479438137288670256964",
"35660343372397246917403353013",
"44791475616825872944740798413234",
"64911462519379469821754507087299215"
] | [
"nonn"
] | 11 | 0 | 3 | [
"A048144",
"A305919",
"A382737",
"A382738",
"A382739",
"A382847",
"A382853"
] | null | Ilya Gutkovskiy, Apr 06 2025 | 2025-04-08T12:23:51 | oeisdata/seq/A382/A382847.seq | ea55946fea71030d2fdbf64d8be35c4e |
A382848 | a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k)^2 * binomial(n+k,k). | [
"1",
"1",
"-5",
"-35",
"-29",
"751",
"3991",
"-4115",
"-137885",
"-495269",
"2114245",
"25786795",
"50109775",
"-627370925",
"-4643568305",
"-495798035",
"157753390435",
"768269873875",
"-1851203127335",
"-35924154988865",
"-107001450483779",
"763444753890721",
"7510024190977105",
"8899910747771995"
] | [
"sign"
] | 7 | 0 | 3 | [
"A005258",
"A026641",
"A126869",
"A245086",
"A382848",
"A382849"
] | null | Ilya Gutkovskiy, Apr 06 2025 | 2025-04-09T05:40:11 | oeisdata/seq/A382/A382848.seq | 9d290a0c62c85bc48f72734865f85995 |
A382849 | a(n) = Sum_{k=0..n} (-1)^(n-k) * (binomial(n,k) * binomial(n+k,k))^2. | [
"1",
"3",
"1",
"-357",
"-6999",
"-62997",
"444529",
"27783003",
"508019689",
"3206511003",
"-89889084999",
"-3274278527517",
"-49395223500999",
"-66079827133317",
"16197028704290001",
"433384098559415643",
"4988878584849669609",
"-35687369703800052357",
"-2815548294132454060151",
"-58942279760573467233357"
] | [
"sign"
] | 6 | 0 | 2 | [
"A005258",
"A005259",
"A126869",
"A176335",
"A228304",
"A382848",
"A382849"
] | null | Ilya Gutkovskiy, Apr 06 2025 | 2025-04-09T05:40:07 | oeisdata/seq/A382/A382849.seq | d78731ba1d042eaf650452a6b2b974df |
A382850 | a(n) = least k such that binomial(n, k) > binomial(n - 1, h) for 0 <= h <= n - 1. | [
"1",
"1",
"1",
"2",
"2",
"2",
"3",
"3",
"4",
"4",
"4",
"5",
"5",
"6",
"6",
"7",
"7",
"7",
"8",
"8",
"9",
"9",
"10",
"10",
"10",
"11",
"11",
"12",
"12",
"13",
"13",
"14",
"14",
"15",
"15",
"15",
"16",
"16",
"17",
"17",
"18",
"18",
"19",
"19",
"19",
"20",
"20",
"21",
"21",
"22",
"22",
"23",
"23",
"24",
"24",
"25",
"25",
"25",
"26",
"26",
"27",
"27",
"28",
"28",
"29",
"29",
"30",
"30",
"31",
"31"
] | [
"nonn",
"new"
] | 21 | 2 | 4 | [
"A001405",
"A007318",
"A382850",
"A382851"
] | null | Clark Kimberling, Apr 07 2025 | 2025-04-18T21:03:39 | oeisdata/seq/A382/A382850.seq | 2aae4a068e7a90c2f116873b156f41ab |
A382851 | a(n) = least number in row n of Pascal's triangle that exceeds every number in row n-1. | [
"2",
"3",
"4",
"10",
"15",
"21",
"56",
"84",
"210",
"330",
"495",
"1287",
"2002",
"5005",
"8008",
"19448",
"31824",
"50388",
"125970",
"203490",
"497420",
"817190",
"1961256",
"3268760",
"5311735",
"13037895",
"21474180",
"51895935",
"86493225",
"206253075",
"347373600",
"818809200",
"1391975640",
"3247943160",
"5567902560"
] | [
"nonn",
"new"
] | 8 | 2 | 1 | [
"A007318",
"A382850",
"A382851"
] | null | Clark Kimberling, Apr 13 2025 | 2025-04-18T21:03:55 | oeisdata/seq/A382/A382851.seq | edc2e936bf6a917a89ce03defd3dccef |
A382853 | a(n) = Sum_{k=0..n} binomial(n+k-1,k) * (k! * Stirling1(n,k))^2. | [
"1",
"1",
"14",
"588",
"51064",
"7542780",
"1688795184",
"532244030976",
"224335607135616",
"121793234373123840",
"82750681453274478720",
"68773648886955417943296",
"68628724852793337500166144",
"80970628401965472953705395200",
"111490683570184861858636405923840",
"177177650274516448010905794637332480"
] | [
"nonn"
] | 15 | 0 | 3 | [
"A382792",
"A382804",
"A382806",
"A382853"
] | null | Seiichi Manyama, Apr 06 2025 | 2025-04-07T09:26:19 | oeisdata/seq/A382/A382853.seq | 22377001af020daaa9fcc31092fc5bd4 |
A382854 | Decimal expansion of (1-log(2))/2. | [
"1",
"5",
"3",
"4",
"2",
"6",
"4",
"0",
"9",
"7",
"2",
"0",
"0",
"2",
"7",
"3",
"4",
"5",
"2",
"9",
"1",
"3",
"8",
"3",
"9",
"3",
"9",
"2",
"7",
"0",
"9",
"1",
"1",
"7",
"1",
"5",
"9",
"6",
"2",
"2",
"4",
"9",
"9",
"3",
"2",
"8",
"1",
"9",
"8",
"7",
"2",
"3",
"7",
"2",
"9",
"3",
"9",
"6",
"5",
"9",
"9",
"9",
"5",
"2",
"5",
"3",
"3",
"0",
"3",
"1",
"8",
"9",
"0",
"1",
"5",
"1",
"5",
"2",
"6",
"4",
"2",
"1",
"9",
"7",
"0",
"6",
"8"
] | [
"nonn",
"cons"
] | 13 | 0 | 2 | [
"A187832",
"A372858",
"A382854",
"A382884"
] | null | Sean A. Irvine, Apr 06 2025 | 2025-04-07T16:51:26 | oeisdata/seq/A382/A382854.seq | 47df28116da2f59652bc68c9d58b86f6 |
A382855 | Number of minimum connected dominating sets in the n-diagonal intersection graph. | [
"3",
"1",
"40",
"54",
"1862",
"32"
] | [
"nonn",
"more"
] | 15 | 3 | 1 | null | null | Eric W. Weisstein, Apr 07 2025 | 2025-04-07T11:07:08 | oeisdata/seq/A382/A382855.seq | 61800f8b8e9854252964ecaf19a7bc88 |
A382856 | Numbers whose prime indices do not have a mode of 1. | [
"1",
"3",
"5",
"7",
"9",
"11",
"13",
"15",
"17",
"18",
"19",
"21",
"23",
"25",
"27",
"29",
"31",
"33",
"35",
"37",
"39",
"41",
"43",
"45",
"47",
"49",
"50",
"51",
"53",
"54",
"55",
"57",
"59",
"61",
"63",
"65",
"67",
"69",
"71",
"73",
"75",
"77",
"79",
"81",
"83",
"85",
"87",
"89",
"90",
"91",
"93",
"95",
"97",
"98",
"99",
"101",
"103",
"105",
"107",
"108",
"109",
"111",
"113",
"115"
] | [
"nonn"
] | 9 | 1 | 2 | [
"A000265",
"A001222",
"A002865",
"A007814",
"A024556",
"A051903",
"A056239",
"A091602",
"A106529",
"A112798",
"A116598",
"A240312",
"A241131",
"A327473",
"A327476",
"A356862",
"A359178",
"A360013",
"A360014",
"A360015",
"A362605",
"A362611",
"A362613",
"A362614",
"A363486",
"A364061",
"A364062",
"A364158",
"A364159",
"A381437",
"A381542",
"A382526",
"A382856"
] | null | Gus Wiseman, Apr 07 2025 | 2025-04-07T09:26:41 | oeisdata/seq/A382/A382856.seq | 7252946763687136705f46ee7ad160b6 |
A382857 | Number of ways to permute the prime indices of n so that the run-lengths are all equal. | [
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"1",
"1",
"1",
"2",
"2",
"1",
"0",
"1",
"2",
"1",
"1",
"1",
"6",
"1",
"1",
"2",
"2",
"2",
"4",
"1",
"2",
"2",
"0",
"1",
"6",
"1",
"1",
"1",
"2",
"1",
"0",
"1",
"1",
"2",
"1",
"1",
"0",
"2",
"0",
"2",
"2",
"1",
"6",
"1",
"2",
"1",
"1",
"2",
"6",
"1",
"1",
"2",
"6",
"1",
"1",
"1",
"2",
"1",
"1",
"2",
"6",
"1",
"0",
"1",
"2",
"1",
"6",
"2",
"2"
] | [
"nonn",
"changed"
] | 10 | 0 | 7 | [
"A000720",
"A000961",
"A001221",
"A001222",
"A003242",
"A003963",
"A005811",
"A008480",
"A044813",
"A047966",
"A056239",
"A112798",
"A164707",
"A181821",
"A238130",
"A238279",
"A239455",
"A304442",
"A328592",
"A329738",
"A335407",
"A351201",
"A351293",
"A351294",
"A351295",
"A353744",
"A353833",
"A382771",
"A382773",
"A382774",
"A382857",
"A382858",
"A382876",
"A382877",
"A382878",
"A382879",
"A383089",
"A383112"
] | null | Gus Wiseman, Apr 09 2025 | 2025-04-21T10:47:15 | oeisdata/seq/A382/A382857.seq | f491c907235eb4bb40ddf47c6a199df2 |
A382858 | Number of ways to permute a multiset whose multiplicities are the prime indices of n so that the run-lengths are all equal. | [
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"6",
"4",
"0",
"1",
"6",
"1",
"0",
"1",
"24",
"1",
"12",
"1",
"2",
"1",
"0",
"1",
"36",
"4",
"0",
"36",
"0",
"1",
"10",
"1",
"120",
"0",
"0",
"1",
"84",
"1",
"0",
"0",
"24",
"1",
"3",
"1",
"0",
"38",
"0",
"1",
"240",
"6",
"18",
"0",
"0",
"1",
"246",
"0",
"6",
"0",
"0",
"1",
"96",
"1",
"0",
"30",
"720",
"1",
"0",
"1",
"0",
"0",
"14",
"1",
"660",
"1",
"0",
"74",
"0",
"1",
"0",
"1"
] | [
"nonn"
] | 6 | 1 | 4 | [
"A000720",
"A000961",
"A001221",
"A001222",
"A003242",
"A003963",
"A044813",
"A047966",
"A048767",
"A056239",
"A098859",
"A112798",
"A140690",
"A181821",
"A182854",
"A238130",
"A304442",
"A305936",
"A329738",
"A329739",
"A335125",
"A335407",
"A351202",
"A351291",
"A351596",
"A353744",
"A353833",
"A382771",
"A382772",
"A382773",
"A382774",
"A382857",
"A382858",
"A382878",
"A382879",
"A382912",
"A382913",
"A382914",
"A382915"
] | null | Gus Wiseman, Apr 09 2025 | 2025-04-10T23:22:30 | oeisdata/seq/A382/A382858.seq | 513606d48b461dd6f7fc62790dd6ca73 |
A382859 | a(n) = Sum_{k=0..n} binomial(n,k) * binomial((n-1)*(k+1),n-k). | [
"1",
"1",
"5",
"37",
"345",
"3851",
"49468",
"713931",
"11391985",
"198523495",
"3741919446",
"75702725440",
"1633591960883",
"37404262517506",
"904734768056239",
"23030071358784701",
"614912094171482849",
"17172036245893988575",
"500281954849350450946",
"15170753984617328108901"
] | [
"nonn",
"easy"
] | 17 | 0 | 3 | [
"A121673",
"A121674",
"A121675",
"A381425",
"A382859"
] | null | Seiichi Manyama, Apr 07 2025 | 2025-04-09T09:57:09 | oeisdata/seq/A382/A382859.seq | c12db201602fc641841794315a1da89c |
A382860 | Number of odd Ulam numbers <= 10^n. | [
"2",
"12",
"60",
"398",
"3780",
"36868",
"368904",
"3696883",
"36977302",
"369860633"
] | [
"nonn",
"more"
] | 8 | 1 | 1 | [
"A002858",
"A307331",
"A382797",
"A382860",
"A382861"
] | null | Shyam Sunder Gupta, Apr 07 2025 | 2025-04-13T16:14:15 | oeisdata/seq/A382/A382860.seq | 413a832b0c3a4440fca99bd18271c4b6 |
A382861 | Number of even Ulam numbers <= 10^n. | [
"4",
"14",
"65",
"429",
"3804",
"37216",
"371464",
"3702470",
"36999540",
"369917405"
] | [
"nonn",
"more"
] | 7 | 1 | 1 | [
"A002858",
"A307331",
"A382798",
"A382860",
"A382861"
] | null | Shyam Sunder Gupta, Apr 07 2025 | 2025-04-13T16:14:51 | oeisdata/seq/A382/A382861.seq | 93cda639c485205590db571c24a10bcc |
A382862 | Prime numbers whose congruence speed of tetration equals 1. | [
"2",
"3",
"11",
"13",
"17",
"19",
"23",
"29",
"31",
"37",
"41",
"47",
"53",
"59",
"61",
"67",
"71",
"73",
"79",
"83",
"89",
"97",
"103",
"109",
"113",
"127",
"131",
"137",
"139",
"163",
"167",
"173",
"179",
"181",
"191",
"197",
"211",
"223",
"227",
"229",
"233",
"239",
"241",
"263",
"269",
"271",
"277",
"281",
"283",
"311",
"313",
"317",
"331",
"337",
"347",
"353",
"359"
] | [
"nonn",
"base",
"new"
] | 38 | 1 | 1 | [
"A000040",
"A317905",
"A321131",
"A373387",
"A382862"
] | null | Marco Ripà and Gabriele Di Pietro, Apr 13 2025 | 2025-04-24T13:33:09 | oeisdata/seq/A382/A382862.seq | 3c5e294efcc659702c79ef90ad2a4fe4 |
A382863 | a(2*k-1) and a(2*k) are a pair of prime numbers where 9*a(2*k-1) and 8*a(2*k) are neighboring integers. | [
"17",
"19",
"47",
"53",
"79",
"89",
"97",
"109",
"113",
"127",
"223",
"251",
"239",
"269",
"241",
"271",
"337",
"379",
"353",
"397",
"383",
"431",
"433",
"487",
"463",
"521",
"607",
"683",
"673",
"757",
"719",
"809",
"863",
"971",
"881",
"991",
"1087",
"1223",
"1153",
"1297",
"1279",
"1439",
"1297",
"1459",
"1327",
"1493",
"1361",
"1531",
"1423",
"1601"
] | [
"nonn",
"tabf"
] | 7 | 1 | 1 | null | null | Steven Lu, Apr 07 2025 | 2025-04-13T16:17:11 | oeisdata/seq/A382/A382863.seq | 409c3beb54a86f367cc91f3e355252f4 |
A382864 | Triangle read by rows: T(n,k) = T(n-k,k-1) + T(n-k,k) with T(0,0) = 1 for 0 <= k <= A003056(n). | [
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"2",
"0",
"1",
"2",
"1",
"0",
"1",
"3",
"1",
"0",
"1",
"3",
"2",
"0",
"1",
"4",
"3",
"0",
"1",
"4",
"4",
"1",
"0",
"1",
"5",
"5",
"1",
"0",
"1",
"5",
"7",
"2",
"0",
"1",
"6",
"8",
"3",
"0",
"1",
"6",
"10",
"5",
"0",
"1",
"7",
"12",
"6",
"1",
"0",
"1",
"7",
"14",
"9",
"1",
"0",
"1",
"8",
"16",
"11",
"2",
"0",
"1",
"8",
"19",
"15",
"3",
"0",
"1",
"9",
"21",
"18",
"5",
"0",
"1",
"9",
"24",
"23",
"7"
] | [
"nonn",
"tabf"
] | 23 | 0 | 14 | [
"A000007",
"A000009",
"A000012",
"A003056",
"A004526",
"A008284",
"A026810",
"A026811",
"A026812",
"A026813",
"A026814",
"A026815",
"A026816",
"A069905",
"A291954",
"A291960",
"A291968",
"A292047",
"A292049",
"A382864"
] | null | Seiichi Manyama, Apr 07 2025 | 2025-04-07T09:26:29 | oeisdata/seq/A382/A382864.seq | 36a69eee9ef43f988815e5dabaa0fff2 |
A382868 | a(1) = 1, a(2) = 2. For n > 2 a(n) is the smallest novel number divisible by the smallest prime p which divides a(n-1) but does not divide a(n-2). If no such prime exists a(n) is the least novel k such that gcd(k, a(n-1)) > 1. | [
"1",
"2",
"4",
"6",
"3",
"9",
"12",
"8",
"10",
"5",
"15",
"18",
"14",
"7",
"21",
"24",
"16",
"20",
"25",
"30",
"22",
"11",
"33",
"27",
"36",
"26",
"13",
"39",
"42",
"28",
"32",
"34",
"17",
"51",
"45",
"35",
"49",
"56",
"38",
"19",
"57",
"48",
"40",
"50",
"44",
"55",
"60",
"46",
"23",
"69",
"54",
"52",
"65",
"70",
"58",
"29",
"87",
"63",
"77",
"66",
"62",
"31",
"93",
"72",
"64",
"68",
"85",
"75"
] | [
"nonn",
"changed"
] | 18 | 1 | 2 | [
"A064413",
"A382868"
] | null | David James Sycamore, Apr 07 2025 | 2025-04-20T09:00:35 | oeisdata/seq/A382/A382868.seq | a62a0a9844b7b001fd56f63ba9348c49 |
A382869 | Numbers k >= 1 such that A018804(k) is a Fibonacci number (A000045). | [
"1",
"2",
"3",
"4",
"7",
"9",
"11",
"1751",
"2031",
"45012",
"105772",
"1266256",
"1490601",
"1774525"
] | [
"nonn",
"more"
] | 10 | 1 | 2 | [
"A000045",
"A005382",
"A018804",
"A382869"
] | null | Ctibor O. Zizka, Apr 07 2025 | 2025-04-13T16:19:53 | oeisdata/seq/A382/A382869.seq | 412104cddadffe78519296b4074cb779 |
A382870 | Minimum period of an optimum covering of the set of integers by translates of its subset with diameter no greater than n, maximized over such subsets. | [
"1",
"2",
"4",
"5",
"8",
"8",
"13",
"13",
"27",
"27",
"45",
"53",
"66",
"109",
"129",
"147",
"147",
"170",
"192",
"250",
"286",
"317"
] | [
"nonn",
"more"
] | 5 | 0 | 2 | null | null | Andrey Zabolotskiy, Apr 07 2025 | 2025-04-07T10:06:49 | oeisdata/seq/A382/A382870.seq | 6ffca38a47e7c19d9e829852c1204f6e |
A382871 | Number of ways to partition distinct prime numbers into two disjoint sets such that the sum of each set equals n. | [
"1",
"0",
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"1",
"1",
"1",
"1",
"1",
"2",
"3",
"3",
"2",
"3",
"4",
"6",
"2",
"5",
"0",
"5",
"9",
"7",
"14",
"8",
"6",
"10",
"9",
"21",
"19",
"11",
"18",
"15",
"29",
"34",
"35",
"34",
"24",
"31",
"51",
"55",
"48",
"76",
"34",
"60",
"93",
"89",
"97",
"91",
"76",
"83",
"156",
"164",
"189",
"145",
"157",
"172",
"186",
"283",
"276",
"218",
"242",
"280",
"405",
"433",
"476",
"446"
] | [
"nonn"
] | 34 | 0 | 19 | [
"A000607",
"A108796",
"A382871",
"A382954"
] | null | Seiichi Manyama, Apr 09 2025 | 2025-04-10T08:34:33 | oeisdata/seq/A382/A382871.seq | fd4b48ed68c60606fac108399d41551c |
A382872 | For n >= 1, a(n) is the number of divisors (A000005) of the Pillai's arithmetical function: Sum_{k=1..n} gcd(k, n) (A018804). | [
"1",
"2",
"2",
"4",
"3",
"4",
"2",
"6",
"4",
"4",
"4",
"8",
"3",
"4",
"6",
"10",
"4",
"6",
"2",
"12",
"4",
"6",
"6",
"9",
"4",
"6",
"5",
"8",
"4",
"8",
"2",
"10",
"8",
"6",
"6",
"16",
"2",
"4",
"4",
"18",
"5",
"8",
"4",
"16",
"8",
"8",
"4",
"20",
"4",
"8",
"8",
"12",
"8",
"6",
"8",
"12",
"4",
"6",
"6",
"24",
"3",
"4",
"8",
"9",
"9",
"12",
"4",
"16",
"9",
"8",
"4",
"24",
"4",
"4",
"6",
"8",
"8",
"8",
"2",
"20"
] | [
"nonn"
] | 11 | 1 | 2 | [
"A000005",
"A005408",
"A018804",
"A065091",
"A382872"
] | null | Ctibor O. Zizka, Apr 07 2025 | 2025-04-13T16:20:02 | oeisdata/seq/A382/A382872.seq | 8212b5ed9434d2b13a03ae0211d4741b |
A382873 | a(n) = A019565(A014311(n)). | [
"30",
"42",
"70",
"105",
"66",
"110",
"165",
"154",
"231",
"385",
"78",
"130",
"195",
"182",
"273",
"455",
"286",
"429",
"715",
"1001",
"102",
"170",
"255",
"238",
"357",
"595",
"374",
"561",
"935",
"1309",
"442",
"663",
"1105",
"1547",
"2431",
"114",
"190",
"285",
"266",
"399",
"665",
"418",
"627",
"1045",
"1463",
"494",
"741",
"1235",
"1729",
"2717",
"646"
] | [
"nonn"
] | 10 | 1 | 1 | [
"A007304",
"A014311",
"A019565",
"A382873"
] | null | Chai Wah Wu, Apr 07 2025 | 2025-04-10T07:06:29 | oeisdata/seq/A382/A382873.seq | d5746a998182d4d87547da2b4debbdee |
A382874 | Expansion of g.f. 2-hypergeom([3/2,7/2],[-1/2],4*x). | [
"1",
"42",
"1890",
"32340",
"378378",
"3567564",
"29201172",
"216164520",
"1484052570",
"9607866268",
"59342703420",
"352648983960",
"2029131058500",
"11360419371000",
"62125264788840",
"332868702695760",
"1751865025825530",
"9075126224864700",
"46353422502086700",
"233788539957892920"
] | [
"nonn"
] | 18 | 0 | 2 | [
"A001700",
"A002421",
"A002423",
"A002457",
"A382874"
] | null | Karol A. Penson, Apr 07 2025 | 2025-04-08T13:59:50 | oeisdata/seq/A382/A382874.seq | a39466eb32fd4dc3d53888ff2d00e449 |
A382875 | Numbers which are a multiple of 2^k - 1 for some k > 1. | [
"0",
"3",
"6",
"7",
"9",
"12",
"14",
"15",
"18",
"21",
"24",
"27",
"28",
"30",
"31",
"33",
"35",
"36",
"39",
"42",
"45",
"48",
"49",
"51",
"54",
"56",
"57",
"60",
"62",
"63",
"66",
"69",
"70",
"72",
"75",
"77",
"78",
"81",
"84",
"87",
"90",
"91",
"93",
"96",
"98",
"99",
"102",
"105",
"108",
"111",
"112",
"114",
"117",
"119",
"120",
"123",
"124",
"126",
"127",
"129",
"132",
"133",
"135",
"138",
"140"
] | [
"nonn"
] | 5 | 1 | 2 | [
"A000225",
"A001477",
"A161788",
"A161789",
"A161790",
"A382875"
] | null | Stefano Spezia, Apr 07 2025 | 2025-04-12T12:33:18 | oeisdata/seq/A382/A382875.seq | 29ce964764aaa5e8d618ac5b17712472 |
A382876 | Number of ways to permute the prime indices of n so that the run-sums are all different. | [
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"0",
"1",
"2",
"2",
"1",
"1",
"2",
"1",
"2",
"2",
"2",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"6",
"1",
"1",
"2",
"2",
"2",
"2",
"1",
"2",
"2",
"2",
"1",
"6",
"1",
"2",
"2",
"2",
"1",
"4",
"1",
"2",
"2",
"2",
"1",
"4",
"2",
"4",
"2",
"2",
"1",
"0",
"1",
"2",
"0",
"1",
"2",
"6",
"1",
"2",
"2",
"6",
"1",
"4",
"1",
"2",
"2",
"2",
"2",
"6",
"1",
"2",
"1",
"2",
"1",
"0",
"2",
"2",
"2"
] | [
"nonn",
"changed"
] | 22 | 1 | 6 | [
"A000720",
"A000961",
"A001221",
"A001222",
"A044813",
"A056239",
"A098859",
"A112798",
"A130091",
"A304442",
"A329738",
"A329739",
"A351013",
"A351202",
"A351596",
"A353832",
"A353837",
"A353838",
"A353847",
"A353848",
"A353850",
"A353851",
"A353852",
"A353932",
"A354580",
"A354584",
"A381636",
"A382076",
"A382771",
"A382857",
"A382876",
"A382877",
"A382879",
"A383100"
] | null | Gus Wiseman, Apr 12 2025 | 2025-04-27T09:09:03 | oeisdata/seq/A382/A382876.seq | ba0f1d58d9f8b3cf4e86c4173b8c3a18 |
A382877 | Number of ways to permute the prime indices of n so that the run-sums are all equal. | [
"1",
"1",
"1",
"1",
"1",
"0",
"1",
"1",
"1",
"0",
"1",
"2",
"1",
"0",
"0",
"1",
"1",
"0",
"1",
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"1",
"1",
"0",
"0",
"0",
"1",
"1",
"0",
"0",
"2",
"1",
"0",
"1",
"0",
"0",
"0",
"1",
"1",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"2",
"1",
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"1",
"0",
"0",
"0",
"0"
] | [
"nonn",
"new"
] | 7 | 1 | 12 | [
"A000720",
"A000961",
"A001221",
"A001222",
"A044813",
"A056239",
"A112798",
"A130091",
"A304442",
"A329738",
"A329739",
"A351596",
"A353832",
"A353833",
"A353837",
"A353838",
"A353847",
"A353848",
"A353850",
"A353851",
"A353852",
"A353932",
"A354584",
"A381871",
"A382076",
"A382771",
"A382857",
"A382876",
"A382877",
"A382879",
"A383015",
"A383098",
"A383099",
"A383100",
"A383110"
] | null | Gus Wiseman, Apr 14 2025 | 2025-04-17T23:21:24 | oeisdata/seq/A382/A382877.seq | a2a8ab15e137039321a2f42a5510bc5f |
A382878 | Set of positions of first appearances in A382857 (permutations of prime indices with equal run-lengths). | [
"1",
"6",
"24",
"30",
"36",
"180",
"210",
"360",
"420",
"720",
"1080",
"1260",
"1800",
"2160",
"2310",
"2520",
"3600",
"4620",
"5040",
"5400",
"6300",
"7560",
"10800",
"12600",
"13860",
"15120",
"21600",
"25200",
"25920",
"27000",
"27720",
"30030",
"32400",
"37800",
"44100",
"45360",
"46656",
"50400",
"54000",
"55440",
"60060",
"60480",
"64800"
] | [
"nonn"
] | 6 | 1 | 2 | [
"A000720",
"A001221",
"A001222",
"A003242",
"A044813",
"A048767",
"A056239",
"A098859",
"A112798",
"A130091",
"A140690",
"A238130",
"A239455",
"A305936",
"A329738",
"A329739",
"A351013",
"A351202",
"A351293",
"A351294",
"A351295",
"A351596",
"A353744",
"A381432",
"A381433",
"A382771",
"A382772",
"A382773",
"A382857",
"A382858",
"A382876",
"A382878",
"A382879"
] | null | Gus Wiseman, Apr 09 2025 | 2025-04-10T23:17:13 | oeisdata/seq/A382/A382878.seq | a1c9e52fcf00ccc7a1f544b98d940374 |
A382879 | Positions of 0 in A382857 (permutations of prime indices with equal run-lengths). | [
"24",
"40",
"48",
"54",
"56",
"80",
"88",
"96",
"104",
"112",
"135",
"136",
"152",
"160",
"162",
"176",
"184",
"189",
"192",
"208",
"224",
"232",
"240",
"248",
"250",
"272",
"288",
"296",
"297",
"304",
"320",
"328",
"336",
"344",
"351",
"352",
"368",
"375",
"376",
"384",
"405",
"416",
"424",
"448",
"459",
"464",
"472",
"480",
"486",
"488",
"496",
"513",
"528",
"536"
] | [
"nonn",
"changed"
] | 8 | 1 | 1 | [
"A000720",
"A000961",
"A001221",
"A001222",
"A003242",
"A005811",
"A008480",
"A047966",
"A056239",
"A112798",
"A130091",
"A164707",
"A238279",
"A239455",
"A297770",
"A304442",
"A328592",
"A329739",
"A351201",
"A351290",
"A351291",
"A351293",
"A351294",
"A351295",
"A351596",
"A353744",
"A353833",
"A382773",
"A382857",
"A382858",
"A382876",
"A382877",
"A382878",
"A382879",
"A382914",
"A382915",
"A383013",
"A383100"
] | null | Gus Wiseman, Apr 09 2025 | 2025-04-21T10:47:08 | oeisdata/seq/A382/A382879.seq | 75c68f53c557f8b3c0226c67435ddb2b |
A382880 | Symmetric triangle read by rows refining A109113. | [
"1",
"1",
"1",
"6",
"6",
"1",
"1",
"11",
"33",
"33",
"11",
"1",
"1",
"16",
"85",
"189",
"189",
"85",
"16",
"1",
"1",
"21",
"162",
"590",
"1107",
"1107",
"590",
"162",
"21",
"1",
"1",
"26",
"264",
"1361",
"3919",
"6588",
"6588",
"3919",
"1361",
"264",
"26",
"1",
"1",
"31",
"391",
"2627",
"10400",
"25484",
"39663",
"39663",
"25484",
"10400",
"2627",
"391",
"31",
"1"
] | [
"nonn",
"tabf"
] | 13 | 0 | 4 | [
"A109113",
"A382880"
] | null | F. Chapoton, Apr 07 2025 | 2025-04-12T12:48:15 | oeisdata/seq/A382/A382880.seq | dbdc38c5716f32ab4a72aa4904f13e4a |
A382882 | Triangle read by rows: T(n, k) = k^ord(n, k) where ord(n, k) is the p-adic order if n and k >= 2, 1 if k = 1, and 0^n if k = 0. | [
"0",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"3",
"1",
"1",
"4",
"1",
"4",
"1",
"1",
"1",
"1",
"1",
"5",
"1",
"1",
"2",
"3",
"1",
"1",
"6",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"7",
"1",
"1",
"8",
"1",
"4",
"1",
"1",
"1",
"8",
"1",
"1",
"1",
"9",
"1",
"1",
"1",
"1",
"1",
"9",
"1",
"1",
"2",
"1",
"1",
"5",
"1",
"1",
"1",
"1",
"10",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"11",
"1",
"1",
"4",
"3",
"4",
"1",
"6",
"1",
"1",
"1",
"1",
"1",
"12"
] | [
"nonn",
"tabl"
] | 7 | 0 | 6 | [
"A286563",
"A364813",
"A381886",
"A382882"
] | null | Peter Luschny, Apr 07 2025 | 2025-04-08T08:49:13 | oeisdata/seq/A382/A382882.seq | 245808845c2484a1f0fce4dce12cf3fb |
A382884 | Decimal expansion of 1/6 + Pi/(12*sqrt(3)) - log(3)/4. | [
"0",
"4",
"3",
"1",
"6",
"3",
"5",
"4",
"1",
"5",
"1",
"9",
"1",
"5",
"7",
"3",
"9",
"8",
"0",
"3",
"4",
"0",
"2",
"8",
"5",
"4",
"5",
"5",
"7",
"2",
"8",
"8",
"1",
"5",
"5",
"1",
"5",
"2",
"8",
"4",
"6",
"6",
"2",
"1",
"4",
"5",
"5",
"2",
"0",
"4",
"1",
"0",
"1",
"8",
"3",
"6",
"3",
"8",
"1",
"6",
"8",
"2",
"7",
"8",
"7",
"2",
"9",
"7",
"0",
"0",
"2",
"5",
"1",
"2",
"2",
"5",
"4",
"3",
"9",
"1",
"5",
"2",
"5",
"5",
"2",
"7",
"3"
] | [
"nonn",
"cons"
] | 12 | 0 | 2 | [
"A187832",
"A382854",
"A382884"
] | null | Sean A. Irvine, Apr 07 2025 | 2025-04-08T15:44:17 | oeisdata/seq/A382/A382884.seq | 3f92207367d3a9b6f892a2d4d32fb4da |
A382885 | G.f. A(x) satisfies A(x) = 1/( 1 - x * (1+x) * A(x) )^3. | [
"1",
"3",
"18",
"121",
"900",
"7110",
"58598",
"498153",
"4336533",
"38463732",
"346368351",
"3158325168",
"29102914959",
"270582713670",
"2535191045652",
"23913087584045",
"226892934532149",
"2164080724942155",
"20737076963936828",
"199542537271568802",
"1927347504059464995",
"18679645863925666721"
] | [
"nonn"
] | 22 | 0 | 2 | [
"A052709",
"A365178",
"A371483",
"A371576",
"A382885"
] | null | Seiichi Manyama, Apr 08 2025 | 2025-04-08T08:47:26 | oeisdata/seq/A382/A382885.seq | e6ee5e094d45845b4d672031ee59be46 |
A382886 | G.f. A(x) satisfies A(x) = 1/( 1 - x * (1+x)^2 * A(x) )^3. | [
"1",
"3",
"21",
"154",
"1248",
"10710",
"95751",
"882297",
"8320812",
"79927938",
"779303829",
"7692585186",
"76726084742",
"772066751871",
"7828529324175",
"79908510600542",
"820435635949686",
"8467306916189517",
"87791572491261912",
"914032693961190414",
"9552050623400554164",
"100162810727306404897"
] | [
"nonn"
] | 24 | 0 | 2 | [
"A073155",
"A378786",
"A382406",
"A382886",
"A382893"
] | null | Seiichi Manyama, Apr 08 2025 | 2025-04-08T08:47:21 | oeisdata/seq/A382/A382886.seq | f9dbafddf816be9984072b050e70c4e8 |
A382887 | Numbers k such that (k*2^d + 1)*(d*2^k + 1) is semiprime for some divisor d of k. | [
"1",
"2",
"8",
"12",
"30",
"51",
"63",
"141",
"201",
"209",
"534",
"4713",
"5795",
"6611",
"7050",
"18496",
"24105",
"32292",
"32469",
"52782",
"59656",
"80190",
"90825"
] | [
"nonn",
"more",
"new"
] | 25 | 1 | 2 | [
"A001358",
"A002064",
"A005849",
"A382646",
"A382887"
] | null | Juri-Stepan Gerasimov, Apr 07 2025 | 2025-04-16T05:42:04 | oeisdata/seq/A382/A382887.seq | 7b449d80085602b29ccdd461d7e2254f |
A382888 | The squarefree kernel of the n-th cubefree number. | [
"1",
"2",
"3",
"2",
"5",
"6",
"7",
"3",
"10",
"11",
"6",
"13",
"14",
"15",
"17",
"6",
"19",
"10",
"21",
"22",
"23",
"5",
"26",
"14",
"29",
"30",
"31",
"33",
"34",
"35",
"6",
"37",
"38",
"39",
"41",
"42",
"43",
"22",
"15",
"46",
"47",
"7",
"10",
"51",
"26",
"53",
"55",
"57",
"58",
"59",
"30",
"61",
"62",
"21",
"65",
"66",
"67",
"34",
"69",
"70",
"71",
"73",
"74",
"15",
"38",
"77",
"78",
"79",
"82"
] | [
"nonn",
"easy"
] | 9 | 1 | 2 | [
"A002117",
"A004709",
"A005117",
"A007947",
"A371188",
"A382888",
"A382889",
"A382890",
"A382891"
] | null | Amiram Eldar, Apr 07 2025 | 2025-04-08T12:49:59 | oeisdata/seq/A382/A382888.seq | be1cdf8b4dcfcdc4720351a81905b263 |
A382889 | The largest square dividing the n-th cubefree number. | [
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"9",
"1",
"1",
"4",
"1",
"1",
"1",
"1",
"9",
"1",
"4",
"1",
"1",
"1",
"25",
"1",
"4",
"1",
"1",
"1",
"1",
"1",
"1",
"36",
"1",
"1",
"1",
"1",
"1",
"1",
"4",
"9",
"1",
"1",
"49",
"25",
"1",
"4",
"1",
"1",
"1",
"1",
"1",
"4",
"1",
"1",
"9",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"1",
"1",
"25",
"4",
"1",
"1",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"1",
"9",
"1",
"4",
"1",
"1",
"1",
"1",
"49",
"9",
"100"
] | [
"nonn",
"easy"
] | 9 | 1 | 4 | [
"A002117",
"A004709",
"A008833",
"A057521",
"A062503",
"A371188",
"A382888",
"A382889",
"A382890",
"A382891"
] | null | Amiram Eldar, Apr 07 2025 | 2025-04-08T12:23:31 | oeisdata/seq/A382/A382889.seq | 18d0248904bf043c076382a5d1551353 |
A382890 | The square root of the largest square dividing the n-th cubefree number. | [
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"3",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"3",
"1",
"2",
"1",
"1",
"1",
"5",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"6",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"3",
"1",
"1",
"7",
"5",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"3",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"5",
"2",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"3",
"1",
"2",
"1",
"1",
"1",
"1",
"7",
"3",
"10",
"1",
"1"
] | [
"nonn",
"easy"
] | 9 | 1 | 4 | [
"A000188",
"A004709",
"A005117",
"A057521",
"A371188",
"A382888",
"A382889",
"A382890",
"A382891"
] | null | Amiram Eldar, Apr 07 2025 | 2025-04-08T13:02:18 | oeisdata/seq/A382/A382890.seq | 508c4ec54c89295fb725085d1b8d21d7 |
A382891 | The powerfree part of the n-th cubefree number. | [
"1",
"2",
"3",
"1",
"5",
"6",
"7",
"1",
"10",
"11",
"3",
"13",
"14",
"15",
"17",
"2",
"19",
"5",
"21",
"22",
"23",
"1",
"26",
"7",
"29",
"30",
"31",
"33",
"34",
"35",
"1",
"37",
"38",
"39",
"41",
"42",
"43",
"11",
"5",
"46",
"47",
"1",
"2",
"51",
"13",
"53",
"55",
"57",
"58",
"59",
"15",
"61",
"62",
"7",
"65",
"66",
"67",
"17",
"69",
"70",
"71",
"73",
"74",
"3",
"19",
"77",
"78",
"79",
"82",
"83"
] | [
"nonn",
"easy"
] | 9 | 1 | 2 | [
"A002117",
"A004709",
"A005117",
"A007913",
"A055231",
"A371188",
"A382888",
"A382889",
"A382890",
"A382891"
] | null | Amiram Eldar, Apr 07 2025 | 2025-04-08T12:23:22 | oeisdata/seq/A382/A382891.seq | 9c6d2bd0f989c930a739ac55030322cb |
A382892 | G.f. A(x) satisfies A(x) = 1/( 1 - x * (1+x)^3 * A(x) )^3. | [
"1",
"3",
"24",
"190",
"1659",
"15309",
"146986",
"1453536",
"14704917",
"151479031",
"1583533308",
"16756882194",
"179149227231",
"1932144798513",
"20996553430206",
"229678298803028",
"2527034248221849",
"27947027713469307",
"310494250880357488",
"3463870813896354726",
"38787008808135775299"
] | [
"nonn"
] | 10 | 0 | 2 | [
"A360076",
"A366272",
"A382614",
"A382892",
"A382894"
] | null | Seiichi Manyama, Apr 08 2025 | 2025-04-08T08:47:17 | oeisdata/seq/A382/A382892.seq | 75edcba1ab8e6af65dbd18a41d112973 |
A382893 | G.f. A(x) satisfies A(x) = 1/( 1 - x * (1+x)^2 * A(x) )^2. | [
"1",
"2",
"11",
"60",
"365",
"2350",
"15767",
"109048",
"771993",
"5567066",
"40751267",
"302018484",
"2261763205",
"17088919814",
"130108591407",
"997225521136",
"7688232599089",
"59581977618098",
"463890112373563",
"3626778446099756",
"28461425971969693",
"224114796803735774",
"1770236735807921863"
] | [
"nonn"
] | 9 | 0 | 2 | [
"A073155",
"A366221",
"A382886",
"A382893"
] | null | Seiichi Manyama, Apr 08 2025 | 2025-04-08T08:47:13 | oeisdata/seq/A382/A382893.seq | cd8aad5a815d05a1617cf7a1b7a31a4e |
A382894 | G.f. A(x) satisfies A(x) = 1/( 1 - x * (1+x)^3 * A(x) )^2. | [
"1",
"2",
"13",
"78",
"520",
"3664",
"26859",
"202808",
"1566693",
"12323982",
"98381841",
"795023284",
"6490951398",
"53462144788",
"443683640945",
"3706539244272",
"31144893093298",
"263052053436600",
"2231992880546400",
"19016760502183968",
"162629329186013523",
"1395500273826639540"
] | [
"nonn"
] | 9 | 0 | 2 | [
"A360076",
"A366200",
"A382613",
"A382892",
"A382894"
] | null | Seiichi Manyama, Apr 08 2025 | 2025-04-08T08:47:09 | oeisdata/seq/A382/A382894.seq | 7c9c29ea3d13bd9445ff5ec7a79b6b1f |
A382895 | Divide n successively by its nonzero digits from most to least significant, updating the result at each step and skipping any digit that doesn't divide the current value exactly. | [
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"10",
"11",
"6",
"13",
"14",
"3",
"16",
"17",
"18",
"19",
"10",
"21",
"11",
"23",
"3",
"5",
"13",
"27",
"14",
"29",
"10",
"31",
"16",
"11",
"34",
"7",
"2",
"37",
"38",
"13",
"10",
"41",
"21",
"43",
"11",
"9",
"46",
"47",
"12",
"49",
"10",
"51",
"26",
"53",
"54",
"11",
"56",
"57",
"58",
"59",
"10",
"61",
"31",
"21",
"16",
"13",
"11",
"67",
"68",
"69",
"10",
"71",
"36",
"73",
"74",
"15"
] | [
"nonn",
"easy",
"base"
] | 15 | 1 | 10 | [
"A051801",
"A382895",
"A382897"
] | null | Seiichi Manyama, Apr 08 2025 | 2025-04-08T08:46:19 | oeisdata/seq/A382/A382895.seq | 836dbaa9af328609c8aee543b5eeef9c |
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