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stringlengths 4
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2.35k
| offset_a
int64 -14,827
666,262,453B
| offset_b
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635M
⌀ | cross_references
listlengths 1
128
⌀ | former_ids
listlengths 1
3
⌀ | author
stringlengths 7
231
⌀ | timestamp
timestamp[us]date 1999-12-11 03:00:00
2025-07-14 02:38:35
| filename
stringlengths 29
29
| hash
stringlengths 32
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|---|---|---|---|---|---|---|---|---|---|---|---|---|
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"
]
| 30 | 1 | 2 | [
"A350877",
"A382822"
]
| null | Enrique Navarrete, Apr 15 2025 | 2025-04-23T10:21:41 | oeisdata/seq/A382/A382822.seq | 845bc46f34017fe482ec74d75e946802 |
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 | a(n) is the n-th n-almost-prime that is a partial sum of the sequence of n-almost-primes. | [
"2",
"10",
"964",
"1804",
"7820",
"48120",
"830817",
"4895208",
"11308160",
"162802560",
"394129476",
"3763612800",
"19823090472",
"1018716103620",
"9744542956800",
"3989325082624",
"329306801920000",
"2978224618328064",
"11804664377696256",
"128906665137012736"
]
| [
"nonn"
]
| 16 | 1 | 1 | [
"A007504",
"A062198",
"A086046",
"A086047",
"A086052",
"A086059",
"A086061",
"A086062",
"A382831"
]
| null | Robert Israel, Apr 28 2025 | 2025-04-29T13:27:31 | oeisdata/seq/A382/A382831.seq | 5025db0e4f3b9312759b511de4380cf5 |
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"
]
| 53 | 1 | 1 | [
"A002110",
"A034386",
"A054270",
"A064819",
"A382834"
]
| null | Jakub Buczak, Apr 06 2025 | 2025-04-17T19:25:09 | oeisdata/seq/A382/A382834.seq | c3ee2c8e2da46fe62318689ff353e49b |
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"
]
| 53 | 1 | 1 | [
"A000010",
"A071324",
"A382837"
]
| null | Shreyansh Jaiswal, Apr 06 2025 | 2025-06-19T16:42:12 | oeisdata/seq/A382/A382837.seq | a1d51c6a321a8e9ebbf282f71c42ed26 |
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",
"2221417812173570640"
]
| [
"nonn",
"more"
]
| 23 | 0 | 2 | [
"A382693",
"A382839"
]
| null | Mark Bowron, Apr 06 2025 | 2025-05-28T01:04:08 | oeisdata/seq/A382/A382839.seq | 79d9174118b2bacc81cc7d90390cd10f |
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"
]
| 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 | 79da5e279be5d2c6d775e3f6b32dc44c |
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"
]
| 11 | 0 | 3 | [
"A005258",
"A026641",
"A126869",
"A245086",
"A382405",
"A382848",
"A382849"
]
| null | Ilya Gutkovskiy, Apr 06 2025 | 2025-06-08T03:33:37 | oeisdata/seq/A382/A382848.seq | dd3db0e486826eb476bea7deffdae697 |
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"
]
| 21 | 2 | 4 | [
"A001405",
"A007318",
"A382850",
"A382851"
]
| null | Clark Kimberling, Apr 07 2025 | 2025-04-18T21:03:39 | oeisdata/seq/A382/A382850.seq | d6f04f616a5c3a62e1d514d75ba8a5ae |
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"
]
| 12 | 2 | 1 | [
"A007318",
"A382850",
"A382851"
]
| null | Clark Kimberling, Apr 13 2025 | 2025-05-02T23:59:41 | oeisdata/seq/A382/A382851.seq | 840cbb034073fd0cb4b303d3ebfda63c |
A382852 | A greedy expansion of Pi where each numerator a(n) is the denominator of the previous term added, and each a(n) is as small as possible without the sum of terms being greater than Pi. The first numerator is 3. | [
"3",
"1",
"8",
"483",
"16369224",
"22916787881317207695",
"836256632995438687172001339486820832419619085705707"
]
| [
"nonn"
]
| 62 | 0 | 1 | [
"A000796",
"A382852"
]
| null | Nathan James Blackerby, Apr 06 2025 | 2025-05-13T23:31:40 | oeisdata/seq/A382/A382852.seq | 93e602cd00dad4637a402dd635fd7f05 |
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"
]
| 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 | f087b34fd19c8de3ff361b36a9497afa |
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"
]
| 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 | 3240e1f779b23ed1afa70057b6a83108 |
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 |
A382865 | Bitwise XOR of all integers between n and 2n (endpoints included). | [
"0",
"3",
"5",
"4",
"8",
"15",
"13",
"8",
"16",
"27",
"21",
"28",
"24",
"23",
"29",
"16",
"32",
"51",
"37",
"52",
"40",
"63",
"45",
"56",
"48",
"43",
"53",
"44",
"56",
"39",
"61",
"32",
"64",
"99",
"69",
"100",
"72",
"111",
"77",
"104",
"80",
"123",
"85",
"124",
"88",
"119",
"93",
"112",
"96",
"83",
"101",
"84",
"104",
"95",
"109",
"88",
"112",
"75",
"117",
"76",
"120",
"71",
"125",
"64",
"128",
"195"
]
| [
"nonn",
"look"
]
| 69 | 0 | 2 | [
"A010873",
"A038712",
"A047615",
"A048724",
"A065621",
"A114389",
"A174091",
"A181983",
"A382865"
]
| null | Federico Provvedi, May 21 2025 | 2025-06-12T19:29:43 | oeisdata/seq/A382/A382865.seq | 52391e79ba5fe8b04c0ab75a2d1876bf |
A382866 | Numbers k such that (49^k + 2^k)/51 is prime. | [
"13",
"307",
"1187",
"9241",
"94321"
]
| [
"nonn",
"hard",
"more"
]
| 6 | 1 | 1 | [
"A057187",
"A057188",
"A062587",
"A062589",
"A127996",
"A127997",
"A128344",
"A204940",
"A217320",
"A225807",
"A228922",
"A229542",
"A375161",
"A375236",
"A377031",
"A377856",
"A382866"
]
| null | Robert Price, Jun 11 2025 | 2025-06-12T00:55:37 | oeisdata/seq/A382/A382866.seq | a4f900015d500315b8c1eec5eea37e1d |
A382867 | Decimal expansion of (Pi^3)/31. | [
"1",
"0",
"0",
"0",
"2",
"0",
"2",
"4",
"7",
"3",
"5",
"5",
"8",
"0",
"5",
"8",
"7",
"1",
"5",
"3",
"3",
"7",
"9",
"4",
"5",
"6",
"4",
"7",
"3",
"2",
"5",
"8",
"5",
"1",
"4",
"5",
"8",
"1",
"3",
"6",
"2",
"9",
"9",
"6",
"3",
"1",
"1",
"5",
"7",
"5",
"8",
"4",
"1",
"1",
"9",
"1",
"6",
"5",
"9",
"5",
"2",
"8",
"4",
"2",
"0",
"5",
"8",
"2",
"7",
"0",
"8",
"0",
"3",
"7",
"8",
"9",
"2",
"1",
"6",
"3",
"2",
"3",
"7",
"9",
"2",
"4",
"7",
"4",
"2",
"2",
"6",
"8",
"5",
"8",
"1",
"5",
"7",
"6",
"1",
"9",
"1"
]
| [
"nonn",
"cons",
"easy"
]
| 18 | 1 | 5 | [
"A000796",
"A091925",
"A382867"
]
| null | Jason Bard, Jun 12 2025 | 2025-06-13T08:22:38 | oeisdata/seq/A382/A382867.seq | 6487a1ff66910facc9b238dd052aad2c |
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"
]
| 18 | 1 | 2 | [
"A064413",
"A382868"
]
| null | David James Sycamore, Apr 07 2025 | 2025-04-20T09:00:35 | oeisdata/seq/A382/A382868.seq | aba2bb1a3f707e7f2883584e9b87f3a8 |
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 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"
]
| 19 | 1 | 2 | [
"A000005",
"A005382",
"A005408",
"A018804",
"A065091",
"A067756",
"A277201",
"A382872"
]
| null | Ctibor O. Zizka, Apr 07 2025 | 2025-05-21T00:52:14 | oeisdata/seq/A382/A382872.seq | 884dd22c48ed1cd1a087ad8c8afd63a9 |
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",
"changed"
]
| 10 | 1 | 2 | [
"A000225",
"A001477",
"A161788",
"A161789",
"A161790",
"A382875"
]
| null | Stefano Spezia, Apr 07 2025 | 2025-06-30T04:29:09 | oeisdata/seq/A382/A382875.seq | 38c405ccb5366480eb14b7bbe7b5c3d1 |
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"
]
| 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 | cb6f47de6f59f3e85f4181c94fbe1e43 |
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"
]
| 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 | 0ec04e71f94e20e27fe0bbf8fe640398 |
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"
]
| 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 | e690f043cee1759487e78571c1e0fd19 |
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 |
A382881 | Triangle read by rows: T(n, k) = -Sum_{d|n, d<n} V(n, d)*T(d, k) for k >= 1, T(n, 0) = 0^n, T(n, n) = 1, where V(n, d) = 1 if d = 1 otherwise valuation(n, d). | [
"1",
"0",
"1",
"0",
"-1",
"1",
"0",
"-1",
"0",
"1",
"0",
"1",
"-2",
"0",
"1",
"0",
"-1",
"0",
"0",
"0",
"1",
"0",
"1",
"-1",
"-1",
"0",
"0",
"1",
"0",
"-1",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"1",
"-1",
"0",
"-1",
"0",
"0",
"0",
"1",
"0",
"1",
"0",
"-2",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"1",
"-1",
"0",
"0",
"-1",
"0",
"0",
"0",
"0",
"1",
"0",
"-1",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"1",
"0",
"-1",
"0",
"-1",
"0",
"0",
"0",
"0",
"0",
"1"
]
| [
"sign",
"tabl"
]
| 18 | 0 | 13 | [
"A019590",
"A382881",
"A382883",
"A382944"
]
| null | Peter Luschny, Apr 09 2025 | 2025-04-29T16:52:51 | oeisdata/seq/A382/A382881.seq | b1ca193af92d0f4caf7f940b7f461a66 |
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 |
A382883 | a(n) = A382881(n, 1) = -Sum_{d|n, 1<d} A382881(n, d) for n >= 2, otherwise n. | [
"1",
"-1",
"-1",
"1",
"-1",
"1",
"-1",
"1",
"1",
"1",
"-1",
"0",
"-1",
"1",
"1",
"0",
"-1",
"0",
"-1",
"0",
"1",
"1",
"-1",
"0",
"1",
"1",
"1",
"0",
"-1",
"-1",
"-1",
"1",
"1",
"1",
"1",
"-1",
"-1",
"1",
"1",
"0",
"-1",
"-1",
"-1",
"0",
"0",
"1",
"-1",
"0",
"1",
"0",
"1",
"0",
"-1",
"0",
"1",
"0",
"1",
"1",
"-1",
"0",
"-1",
"1",
"0",
"-1",
"1",
"-1",
"-1",
"0",
"1",
"-1",
"-1",
"0",
"-1",
"1",
"0",
"0",
"1"
]
| [
"sign"
]
| 50 | 1 | null | [
"A001221",
"A002321",
"A008683",
"A008966",
"A053810",
"A059404",
"A072774",
"A072776",
"A113704",
"A363914",
"A382881",
"A382883",
"A382940",
"A382941",
"A382942",
"A382943",
"A382944",
"A383016",
"A383017",
"A383018",
"A383104",
"A383105",
"A383106",
"A383123",
"A383124",
"A383210",
"A383211",
"A383575",
"A383576",
"A384667"
]
| null | Peter Luschny, Apr 09 2025 | 2025-06-17T02:57:38 | oeisdata/seq/A382/A382883.seq | e72a0ec1ca257cfd75972a35cb190128 |
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"
]
| 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 | 915497494601f9da84aa49228e5baf31 |
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 |
A382896 | Smith sphenic numbers, i.e., Smith numbers (A006753) that are the product of three distinct prime numbers. | [
"438",
"483",
"627",
"645",
"654",
"663",
"762",
"861",
"915",
"1086",
"1581",
"1626",
"1842",
"2067",
"2265",
"2373",
"2409",
"2679",
"2751",
"3138",
"3246",
"3345",
"3615",
"4173",
"4191",
"4209",
"4974",
"5253",
"5298",
"5397",
"5946",
"6054",
"6315",
"6531",
"6567",
"6585",
"6603",
"6693",
"6702",
"6855",
"6981",
"7026",
"7089",
"7287"
]
| [
"nonn",
"base"
]
| 10 | 1 | 1 | [
"A006753",
"A007304",
"A382896"
]
| null | Shyam Sunder Gupta, Apr 08 2025 | 2025-04-08T09:35:40 | oeisdata/seq/A382/A382896.seq | 4863f885bf16e34787a67e47eaa0e2be |
A382897 | a(n) = n / A382895(n). | [
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"1",
"1",
"2",
"1",
"1",
"5",
"1",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"8",
"5",
"2",
"1",
"2",
"1",
"3",
"1",
"2",
"3",
"1",
"5",
"18",
"1",
"1",
"3",
"4",
"1",
"2",
"1",
"4",
"5",
"1",
"1",
"4",
"1",
"5",
"1",
"2",
"1",
"1",
"5",
"1",
"1",
"1",
"1",
"6",
"1",
"2",
"3",
"4",
"5",
"6",
"1",
"1",
"1",
"7",
"1",
"2",
"1",
"1",
"5",
"1",
"7",
"1",
"1",
"8",
"1",
"2",
"1",
"4",
"5",
"1",
"1",
"8",
"1",
"9",
"1",
"2",
"3",
"1",
"5",
"6",
"1",
"1",
"9"
]
| [
"nonn",
"base",
"easy"
]
| 10 | 1 | 2 | [
"A051801",
"A382895",
"A382897"
]
| null | Seiichi Manyama, Apr 08 2025 | 2025-04-08T08:46:23 | oeisdata/seq/A382/A382897.seq | 89a17bcadd680563125de09ec017d5a8 |
A382898 | Beginning with 13, least prime such that concatenation of first n terms and its digit reversal both are primes. | [
"13",
"151",
"227",
"2083",
"887",
"79",
"2963",
"1579",
"6287",
"1321",
"6719",
"54919",
"26699",
"8647",
"4229",
"3919",
"102161",
"42433",
"1667",
"192193",
"11633",
"186343",
"47339",
"3259",
"65963",
"14293",
"29717",
"61297",
"28493",
"231367",
"43793",
"145021",
"566441",
"475903",
"92381",
"80473",
"139967",
"882061",
"72893",
"709279",
"6053",
"114487",
"1179389",
"204331",
"203351",
"139831",
"396239",
"205327",
"501173",
"951589"
]
| [
"base",
"nonn"
]
| 9 | 1 | 1 | [
"A111382",
"A111383",
"A113584",
"A379354",
"A379355",
"A379761",
"A380227",
"A382898"
]
| null | J.W.L. (Jan) Eerland, Apr 08 2025 | 2025-04-15T04:00:01 | oeisdata/seq/A382/A382898.seq | aba4931903ac090b2c3c9058d4d883b1 |
A382899 | The smallest n-digit prime that turns composite at each step as its digits are successively appended, starting from the first. | [
"2",
"11",
"101",
"1013",
"10007",
"100003",
"1000003",
"10000019",
"100000007",
"1000000007",
"10000000019",
"100000000003",
"1000000000061",
"10000000000037",
"100000000000031",
"1000000000000037",
"10000000000000061",
"100000000000000013",
"1000000000000000003",
"10000000000000000051"
]
| [
"nonn",
"base"
]
| 30 | 1 | 1 | [
"A003617",
"A382899",
"A382981"
]
| null | Jean-Marc Rebert, Apr 08 2025 | 2025-04-16T09:02:08 | oeisdata/seq/A382/A382899.seq | ca868ca62f0d1932496678e2b3ca9e50 |
A382900 | Composites whose prime factors are not all Mersenne primes. | [
"4",
"6",
"8",
"10",
"12",
"14",
"15",
"16",
"18",
"20",
"22",
"24",
"25",
"26",
"28",
"30",
"32",
"33",
"34",
"35",
"36",
"38",
"39",
"40",
"42",
"44",
"45",
"46",
"48",
"50",
"51",
"52",
"54",
"55",
"56",
"57",
"58",
"60",
"62",
"64",
"65",
"66",
"68",
"69",
"70",
"72",
"74",
"75",
"76",
"77",
"78",
"80",
"82",
"84",
"85",
"86",
"87",
"88",
"90",
"91",
"92",
"94",
"95",
"96",
"98",
"99",
"100"
]
| [
"nonn"
]
| 7 | 1 | 1 | [
"A000668",
"A002808",
"A056652",
"A348839",
"A382900"
]
| null | Stefano Spezia, Apr 08 2025 | 2025-04-12T12:36:15 | oeisdata/seq/A382/A382900.seq | ecb3776675341ae794302dff41863a8a |
A382901 | Semiprimes that can be expressed using at most one of each of the semiprime digits 4, 6, 9 using concatenation and the arithmetic operations +, -, *, /, ^. | [
"4",
"6",
"9",
"10",
"15",
"33",
"46",
"49",
"55",
"58",
"65",
"69",
"94",
"469",
"649",
"694",
"4087",
"4105"
]
| [
"nonn",
"base",
"fini",
"full"
]
| 13 | 1 | 1 | null | null | Zak Seidov and Robert Israel, Apr 08 2025 | 2025-04-11T07:58:31 | oeisdata/seq/A382/A382901.seq | 02780740fc263484781fa2e12a427904 |
A382902 | The largest cubefree divisor of the n-th biquadratefree number. | [
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"4",
"9",
"10",
"11",
"12",
"13",
"14",
"15",
"17",
"18",
"19",
"20",
"21",
"22",
"23",
"12",
"25",
"26",
"9",
"28",
"29",
"30",
"31",
"33",
"34",
"35",
"36",
"37",
"38",
"39",
"20",
"41",
"42",
"43",
"44",
"45",
"46",
"47",
"49",
"50",
"51",
"52",
"53",
"18",
"55",
"28",
"57",
"58",
"59",
"60",
"61",
"62",
"63",
"65",
"66",
"67",
"68",
"69",
"70",
"71",
"36"
]
| [
"nonn",
"easy"
]
| 8 | 1 | 2 | [
"A007948",
"A013662",
"A046100",
"A382902",
"A382903",
"A382904",
"A382905",
"A382906"
]
| null | Amiram Eldar, Apr 08 2025 | 2025-04-09T04:19:47 | oeisdata/seq/A382/A382902.seq | 6915ca4cb412acf98966c24084ab4720 |
A382903 | The largest cubefree unitary divisor of the n-th biquadratefree number. | [
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"1",
"9",
"10",
"11",
"12",
"13",
"14",
"15",
"17",
"18",
"19",
"20",
"21",
"22",
"23",
"3",
"25",
"26",
"1",
"28",
"29",
"30",
"31",
"33",
"34",
"35",
"36",
"37",
"38",
"39",
"5",
"41",
"42",
"43",
"44",
"45",
"46",
"47",
"49",
"50",
"51",
"52",
"53",
"2",
"55",
"7",
"57",
"58",
"59",
"60",
"61",
"62",
"63",
"65",
"66",
"67",
"68",
"69",
"70",
"71",
"9",
"73"
]
| [
"nonn",
"easy"
]
| 7 | 1 | 2 | [
"A013662",
"A046100",
"A360539",
"A382902",
"A382903",
"A382904",
"A382905",
"A382906"
]
| null | Amiram Eldar, Apr 08 2025 | 2025-04-09T04:19:43 | oeisdata/seq/A382/A382903.seq | 683ac0527e79a920e8a8652b0ed8a1f4 |
A382904 | The squarefree kernel of the n-th biquadratefree number. | [
"1",
"2",
"3",
"2",
"5",
"6",
"7",
"2",
"3",
"10",
"11",
"6",
"13",
"14",
"15",
"17",
"6",
"19",
"10",
"21",
"22",
"23",
"6",
"5",
"26",
"3",
"14",
"29",
"30",
"31",
"33",
"34",
"35",
"6",
"37",
"38",
"39",
"10",
"41",
"42",
"43",
"22",
"15",
"46",
"47",
"7",
"10",
"51",
"26",
"53",
"6",
"55",
"14",
"57",
"58",
"59",
"30",
"61",
"62",
"21",
"65",
"66",
"67",
"34",
"69",
"70",
"71",
"6",
"73",
"74"
]
| [
"nonn",
"easy"
]
| 7 | 1 | 2 | [
"A007947",
"A013662",
"A046100",
"A382902",
"A382903",
"A382904",
"A382905",
"A382906"
]
| null | Amiram Eldar, Apr 08 2025 | 2025-04-09T04:19:39 | oeisdata/seq/A382/A382904.seq | 22d8b70d46e0ff8853326b91b89922a5 |
A382905 | The powerfree part of the n-th biquadratefree number. | [
"1",
"2",
"3",
"1",
"5",
"6",
"7",
"1",
"1",
"10",
"11",
"3",
"13",
"14",
"15",
"17",
"2",
"19",
"5",
"21",
"22",
"23",
"3",
"1",
"26",
"1",
"7",
"29",
"30",
"31",
"33",
"34",
"35",
"1",
"37",
"38",
"39",
"5",
"41",
"42",
"43",
"11",
"5",
"46",
"47",
"1",
"2",
"51",
"13",
"53",
"2",
"55",
"7",
"57",
"58",
"59",
"15",
"61",
"62",
"7",
"65",
"66",
"67",
"17",
"69",
"70",
"71",
"1",
"73",
"74",
"3",
"19"
]
| [
"nonn",
"easy"
]
| 7 | 1 | 2 | [
"A013662",
"A046100",
"A055231",
"A382902",
"A382903",
"A382904",
"A382905",
"A382906"
]
| null | Amiram Eldar, Apr 08 2025 | 2025-04-09T04:19:39 | oeisdata/seq/A382/A382905.seq | f244056f75dcfaee818a759bf1889ed7 |
A382906 | The powerful part of the n-th biquadratefree number. | [
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"8",
"9",
"1",
"1",
"4",
"1",
"1",
"1",
"1",
"9",
"1",
"4",
"1",
"1",
"1",
"8",
"25",
"1",
"27",
"4",
"1",
"1",
"1",
"1",
"1",
"1",
"36",
"1",
"1",
"1",
"8",
"1",
"1",
"1",
"4",
"9",
"1",
"1",
"49",
"25",
"1",
"4",
"1",
"27",
"1",
"8",
"1",
"1",
"1",
"4",
"1",
"1",
"9",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"72",
"1",
"1",
"25",
"4",
"1",
"1",
"1",
"1",
"1",
"4",
"1",
"1",
"1",
"8",
"1",
"9",
"1"
]
| [
"nonn",
"easy"
]
| 9 | 1 | 4 | [
"A013662",
"A046100",
"A057521",
"A382902",
"A382903",
"A382904",
"A382905",
"A382906"
]
| null | Amiram Eldar, Apr 08 2025 | 2025-04-09T04:19:29 | oeisdata/seq/A382/A382906.seq | cbf7ec715db906fd4b5bda0da5739eeb |
A382907 | Decimal expansion of 1/2 - Pi*(sqrt(2)+1)/16. | [
"0",
"2",
"5",
"9",
"7",
"0",
"2",
"7",
"5",
"5",
"1",
"5",
"7",
"4",
"0",
"0",
"3",
"2",
"1",
"5",
"7",
"5",
"9",
"2",
"2",
"2",
"6",
"6",
"6",
"6",
"2",
"3",
"7",
"7",
"1",
"3",
"5",
"7",
"4",
"2",
"6",
"3",
"0",
"5",
"6",
"9",
"5",
"3",
"0",
"7",
"5",
"2",
"4",
"7",
"2",
"4",
"6",
"2",
"2",
"8",
"7",
"3",
"7",
"5",
"4",
"5",
"9",
"8",
"4",
"3",
"0",
"0",
"0",
"3",
"8",
"3",
"9",
"4",
"8",
"1",
"8",
"1",
"7",
"4",
"7",
"8",
"9"
]
| [
"nonn",
"cons"
]
| 6 | 0 | 2 | [
"A239120",
"A382907"
]
| null | Sean A. Irvine, Apr 08 2025 | 2025-04-30T15:07:35 | oeisdata/seq/A382/A382907.seq | b95dfca9c61e82fd22939f6231feb43b |
A382908 | Lexicographically earliest sequence of positive integers such that the n-th pair of consecutive equal values are separated by a(n) distinct terms, with pairs numbered by their average index. | [
"1",
"2",
"1",
"3",
"2",
"3",
"4",
"1",
"3",
"2",
"5",
"2",
"4",
"3",
"2",
"4",
"6",
"3",
"5",
"1",
"3",
"7",
"5",
"6",
"5",
"2",
"1"
]
| [
"nonn",
"more"
]
| 20 | 1 | 2 | [
"A363654",
"A363708",
"A363757",
"A382908",
"A382911"
]
| null | Neal Gersh Tolunsky, Apr 08 2025 | 2025-04-23T10:37:00 | oeisdata/seq/A382/A382908.seq | 1353f5b690645690a6c2573c28e86659 |
A382909 | Number of possible (area, dinv) interchanging bijections of Dyck paths of length 2n. | [
"1",
"1",
"1",
"1",
"16",
"165112971264",
"7081067777179913483347996561235301491807900639024696524800000000000000000000"
]
| [
"nonn"
]
| 24 | 1 | 5 | null | null | Blake Jackson, Apr 08 2025 | 2025-04-19T06:16:50 | oeisdata/seq/A382/A382909.seq | 048883ac22e83a059523fdb2842e8de5 |
A382910 | a(n) = A003266(n)^2. | [
"1",
"1",
"1",
"4",
"36",
"900",
"57600",
"9734400",
"4292870400",
"4962558182400",
"15011738501760000",
"118907980672440960000",
"2465675887223735746560000",
"133859078241489389944995840000",
"19025256931384645503492313743360000",
"7079298104168226591849489943904256000000",
"6896432754839457130755425769163265163264000000"
]
| [
"nonn",
"easy"
]
| 28 | 0 | 4 | [
"A000045",
"A003266",
"A007598",
"A090281",
"A382910"
]
| null | Edwin Hermann, Apr 08 2025 | 2025-04-15T15:42:45 | oeisdata/seq/A382/A382910.seq | 1a027dfbc9996f18d0df42c76f1cef14 |
A382911 | Lexicographically earliest sequence of positive integers such that the n-th pair of consecutive equal values are separated by a(n) distinct terms, with pairs numbered according to the average index of the pair. | [
"1",
"2",
"1",
"3",
"1",
"2",
"4",
"2",
"3",
"4",
"2",
"5",
"1"
]
| [
"nonn",
"more"
]
| 12 | 1 | 2 | [
"A363654",
"A363708",
"A363757",
"A382908",
"A382911"
]
| null | Neal Gersh Tolunsky, Apr 08 2025 | 2025-04-23T10:37:12 | oeisdata/seq/A382/A382911.seq | 0fb98491a68d3e3aee4a883fd3ca2b32 |
A382912 | Numbers k such that row k of A305936 (a multiset whose multiplicities are the prime indices of k) has no permutation with all distinct run-lengths. | [
"4",
"8",
"9",
"12",
"16",
"18",
"20",
"24",
"27",
"28",
"32",
"36",
"40",
"44",
"45",
"48",
"50",
"52",
"54",
"56",
"60",
"63",
"64",
"68",
"72",
"75",
"76",
"80",
"81",
"84",
"88",
"90",
"92",
"96",
"98",
"99",
"100",
"104",
"108",
"112",
"116",
"117",
"120",
"124",
"125",
"126",
"128",
"132",
"135",
"136",
"140",
"144",
"148",
"150",
"152",
"153",
"156",
"160",
"162",
"164"
]
| [
"nonn"
]
| 15 | 1 | 1 | [
"A000720",
"A001221",
"A001222",
"A048767",
"A056239",
"A112798",
"A181821",
"A239455",
"A305936",
"A329739",
"A335125",
"A351202",
"A351291",
"A351293",
"A351294",
"A351295",
"A351596",
"A381431",
"A381432",
"A381433",
"A381436",
"A381440",
"A381636",
"A381717",
"A381871",
"A382525",
"A382771",
"A382773",
"A382775",
"A382857",
"A382858",
"A382876",
"A382879",
"A382912",
"A382913",
"A382914",
"A382915"
]
| null | Gus Wiseman, Apr 12 2025 | 2025-05-08T19:42:09 | oeisdata/seq/A382/A382912.seq | d6fdee5953e7d139bd2a1be2b84070ef |
A382913 | Numbers k such that row k of A305936 (a multiset whose multiplicities are the prime indices of k) has a permutation with all distinct run-lengths. | [
"1",
"2",
"3",
"5",
"6",
"7",
"10",
"11",
"13",
"14",
"15",
"17",
"19",
"21",
"22",
"23",
"25",
"26",
"29",
"30",
"31",
"33",
"34",
"35",
"37",
"38",
"39",
"41",
"42",
"43",
"46",
"47",
"49",
"51",
"53",
"55",
"57",
"58",
"59",
"61",
"62",
"65",
"66",
"67",
"69",
"70",
"71",
"73",
"74",
"77",
"78",
"79",
"82",
"83",
"85",
"86",
"87",
"89",
"91",
"93",
"94",
"95",
"97",
"101",
"102",
"103"
]
| [
"nonn"
]
| 15 | 1 | 2 | [
"A000720",
"A001221",
"A001222",
"A044813",
"A048767",
"A055396",
"A056239",
"A061395",
"A112798",
"A140690",
"A181821",
"A239455",
"A305936",
"A329739",
"A335125",
"A351293",
"A351294",
"A351295",
"A351596",
"A381431",
"A381432",
"A381436",
"A381440",
"A381636",
"A381717",
"A381871",
"A382525",
"A382771",
"A382773",
"A382775",
"A382858",
"A382876",
"A382879",
"A382912",
"A382913",
"A382914",
"A382915"
]
| null | Gus Wiseman, Apr 12 2025 | 2025-05-08T19:42:04 | oeisdata/seq/A382/A382913.seq | c0c2e0002131de6f03aea3d22175b476 |
A382914 | Numbers k such that it is not possible to permute a multiset whose multiplicities are the prime indices of k so that the run-lengths are all equal. | [
"10",
"14",
"22",
"26",
"28",
"33",
"34",
"38",
"39",
"44",
"46",
"51",
"52",
"55",
"57",
"58",
"62",
"66",
"68",
"69",
"74",
"76",
"78",
"82",
"85",
"86",
"87",
"88",
"92",
"93",
"94",
"95",
"102",
"104",
"106",
"111",
"114",
"115",
"116",
"118",
"119",
"122",
"123",
"124",
"129",
"130",
"134",
"136",
"138",
"141",
"142",
"145",
"146",
"148",
"152",
"153",
"155",
"156"
]
| [
"nonn"
]
| 5 | 1 | 1 | [
"A000720",
"A000961",
"A001221",
"A001222",
"A003963",
"A044813",
"A048767",
"A056239",
"A112798",
"A140690",
"A164707",
"A181821",
"A304442",
"A305936",
"A328592",
"A329738",
"A329739",
"A335125",
"A335126",
"A335127",
"A351013",
"A351291",
"A351596",
"A353744",
"A353833",
"A382771",
"A382772",
"A382773",
"A382857",
"A382858",
"A382877",
"A382878",
"A382879",
"A382912",
"A382913",
"A382914",
"A382915"
]
| null | Gus Wiseman, Apr 09 2025 | 2025-04-11T07:59:22 | oeisdata/seq/A382/A382914.seq | 8c9bf17808d6211f446c8cf3ca369123 |
A382915 | Number of integer partitions of n having no permutation with all equal run-lengths. | [
"0",
"0",
"0",
"0",
"0",
"1",
"2",
"4",
"4",
"9",
"11",
"18",
"21",
"34",
"41",
"55",
"69",
"98",
"120",
"160",
"189",
"249",
"309",
"396",
"472",
"605",
"734",
"913",
"1099",
"1371",
"1632",
"2021",
"2406",
"2937",
"3514",
"4251",
"5039",
"6101",
"7221",
"8646",
"10205",
"12209",
"14347",
"17086",
"20041",
"23713",
"27807",
"32803",
"38262",
"45043",
"52477",
"61471",
"71496"
]
| [
"nonn"
]
| 11 | 0 | 7 | [
"A000009",
"A000041",
"A003242",
"A047966",
"A056239",
"A112798",
"A238279",
"A239455",
"A304442",
"A329738",
"A329739",
"A351201",
"A351290",
"A351293",
"A351294",
"A351295",
"A351596",
"A353744",
"A353833",
"A382773",
"A382857",
"A382879",
"A382914",
"A382915",
"A383013"
]
| null | Gus Wiseman, Apr 12 2025 | 2025-04-26T11:28:02 | oeisdata/seq/A382/A382915.seq | c3ee141bcefe2257bb7c747f77f9fb9b |
A382916 | G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)^3 / (1-x)^2 ). | [
"1",
"1",
"6",
"41",
"316",
"2636",
"23192",
"211926",
"1992032",
"19138016",
"187091252",
"1855104372",
"18612229836",
"188601299149",
"1927443803738",
"19843158497163",
"205602235405524",
"2142401581747657",
"22436439910929038",
"236023405797017891",
"2492914862240934612",
"26426682321857813417"
]
| [
"nonn"
]
| 11 | 0 | 3 | [
"A349331",
"A382916",
"A382917",
"A382920"
]
| null | Seiichi Manyama, Apr 08 2025 | 2025-04-09T07:28:59 | oeisdata/seq/A382/A382916.seq | 30d065856b72d4a37d7b9869823af9c0 |
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