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666,262,453B
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⌀ | timestamp
timestamp[us]date 1999-12-11 03:00:00
2025-07-14 02:38:35
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|---|---|---|---|---|---|---|---|---|---|---|---|---|
A382315 | G.f. satisfies A(x) = x + Sum_{n>=1} A(x^n)^2. | [
"1",
"1",
"2",
"6",
"16",
"51",
"158",
"524",
"1762",
"6089",
"21326",
"75879",
"272794",
"990673",
"3626536",
"13371544",
"49606460",
"185046037",
"693621174",
"2611275523",
"9869097706",
"37431498607",
"142426706634",
"543524937780",
"2079768883112",
"7977836453011",
"30672352831760",
"118175566117561",
"456206491221514",
"1764370233131135"
]
| [
"nonn"
]
| 13 | 1 | 3 | [
"A382315",
"A382321"
]
| null | Paul D. Hanna, Apr 17 2025 | 2025-04-26T04:26:15 | oeisdata/seq/A382/A382315.seq | 3e9e92abed9bcffd84bc01bdc60c43eb |
A382316 | G.f. satisfies A(x) = A(x^2) + A(x^2)^2*A(x^3)/A(x^6), with A(0) = 0 and A'(0) = 1. | [
"1",
"1",
"2",
"2",
"5",
"4",
"9",
"7",
"20",
"14",
"31",
"24",
"60",
"40",
"90",
"66",
"167",
"108",
"241",
"176",
"414",
"263",
"586",
"418",
"987",
"615",
"1352",
"966",
"2185",
"1350",
"2965",
"2079",
"4710",
"2886",
"6262",
"4392",
"9681",
"5906",
"12780",
"8843",
"19492",
"11826",
"25325",
"17512",
"37876",
"22920",
"48956",
"33474",
"72418",
"43680",
"92482",
"63163",
"134737",
"81120",
"171400"
]
| [
"nonn"
]
| 11 | 1 | 3 | null | null | Paul D. Hanna, May 08 2025 | 2025-05-10T09:15:29 | oeisdata/seq/A382/A382316.seq | 8426f4e7687aa5058f466790ef275000 |
A382317 | G.f. satisfies A(x) = A(x^3)/(A(x^2) - A(x^3)), with A(0) = 0, A'(0) = 1. | [
"1",
"1",
"0",
"0",
"1",
"2",
"1",
"-1",
"-2",
"0",
"1",
"-2",
"-6",
"-6",
"0",
"4",
"1",
"-4",
"1",
"16",
"26",
"19",
"8",
"14",
"33",
"35",
"2",
"-38",
"-47",
"-30",
"-45",
"-111",
"-170",
"-146",
"-58",
"-6",
"-23",
"0",
"180",
"451",
"610",
"582",
"547",
"670",
"792",
"546",
"-154",
"-934",
"-1444",
"-1892",
"-2778",
"-4029",
"-4789",
"-4328",
"-2960",
"-1511",
"124",
"3203",
"8437",
"14508",
"19170",
"21741",
"23410"
]
| [
"sign"
]
| 7 | 1 | 6 | [
"A378256",
"A382317"
]
| null | Paul D. Hanna, May 15 2025 | 2025-05-18T07:57:34 | oeisdata/seq/A382/A382317.seq | 6c7acbe4c832f0b709e3072b56ea4bb1 |
A382318 | G.f. satisfies A(x) = x + ( Sum_{n>=1} A(x^n) )^3. | [
"1",
"0",
"1",
"3",
"9",
"25",
"72",
"213",
"635",
"1950",
"6036",
"19021",
"60429",
"194172",
"628384",
"2049225",
"6722658",
"22178631",
"73523028",
"244805574",
"818317630",
"2745167418",
"9238878207",
"31185404902",
"105550046640",
"358134472293",
"1217955671785",
"4150882760334",
"14174481594375",
"48492262770919",
"166181651660136",
"570415046251962"
]
| [
"nonn"
]
| 12 | 1 | 4 | [
"A008683",
"A382318",
"A382319",
"A382320"
]
| null | Paul D. Hanna, Apr 10 2025 | 2025-04-15T06:36:52 | oeisdata/seq/A382/A382318.seq | a11020d318a3cff8a4a71bd594d80f14 |
A382319 | G.f. satisfies A(x) = x/(1-x) + Sum_{n>=1} A(x^n)^3. | [
"1",
"1",
"2",
"4",
"10",
"27",
"73",
"217",
"637",
"1960",
"6037",
"19051",
"60430",
"194245",
"628395",
"2049442",
"6722659",
"22179293",
"73523029",
"244807537",
"818317704",
"2745173455",
"9238878208",
"31185424166",
"105550046650",
"358134532723",
"1217955672422",
"4150882954582",
"14174481594376",
"48492263401289",
"166181651660137",
"570415048301404"
]
| [
"nonn"
]
| 7 | 1 | 3 | [
"A382318",
"A382319",
"A382321"
]
| null | Paul D. Hanna, Apr 10 2025 | 2025-04-11T01:28:06 | oeisdata/seq/A382/A382319.seq | 103b0f46adaef37434d76ecbf0aa8559 |
A382320 | G.f. satisfies A(x) = x + ( Sum_{n>=1} A(x^n) )^2. | [
"1",
"1",
"4",
"14",
"52",
"195",
"774",
"3140",
"13118",
"55861",
"241988",
"1062411",
"4718380",
"21156811",
"95652842",
"435553638",
"1995707806",
"9194770161",
"42570402238",
"197957907525",
"924157498638",
"4329762257151",
"20351029400480",
"95938011359954",
"453492517932696",
"2148971058064469",
"10206782449568402",
"48581518322215785"
]
| [
"nonn"
]
| 6 | 1 | 3 | [
"A008683",
"A382320",
"A382321"
]
| null | Paul D. Hanna, Apr 09 2025 | 2025-04-09T22:55:43 | oeisdata/seq/A382/A382320.seq | 4a7ac3816da19b4f248b34c586db4889 |
A382321 | G.f. satisfies A(x) = x/(1-x) + Sum_{n>=1} A(x^n)^2. | [
"1",
"2",
"5",
"16",
"53",
"201",
"775",
"3156",
"13123",
"55915",
"241989",
"1062626",
"4718381",
"21157587",
"95652899",
"435556794",
"1995707807",
"9194783480",
"42570402239",
"197957963454",
"924157499417",
"4329762499141",
"20351029400481",
"95938012425720",
"453492517932749",
"2148971062782851",
"10206782449581525",
"48581518343373386"
]
| [
"nonn"
]
| 18 | 1 | 2 | [
"A382320",
"A382321"
]
| null | Paul D. Hanna, Apr 09 2025 | 2025-04-15T06:43:06 | oeisdata/seq/A382/A382321.seq | d27f9fbf373851dccc886c9fef63bd53 |
A382322 | G.f. A(x) satisfies -2 = Sum_{n=-oo..+oo} (-1)^n * x^(2*n+1) * (1 + x^n)^(n+1) * A(x)^n. | [
"1",
"2",
"8",
"50",
"308",
"2044",
"14072",
"100172",
"730328",
"5428498",
"40978780",
"313322910",
"2421454020",
"18884988540",
"148443853936",
"1174814738082",
"9353539487160",
"74865615299260",
"602057472027484",
"4862177553583604",
"39416710563473400",
"320650120976612168",
"2616673301770051376",
"21414973020645504142"
]
| [
"nonn"
]
| 13 | 0 | 2 | [
"A356783",
"A380557",
"A382322",
"A382323"
]
| null | Paul D. Hanna, Mar 21 2025 | 2025-03-22T18:50:12 | oeisdata/seq/A382/A382322.seq | ee6e0b2bf15d79d87e8cf453a9563425 |
A382323 | G.f. A(x) satisfies -3 = Sum_{n=-oo..+oo} (-1)^n * x^(2*n+1) * (1 + x^n)^(n+1) * A(x)^n. | [
"1",
"3",
"18",
"150",
"1323",
"12486",
"123069",
"1253595",
"13089576",
"139367370",
"1507353966",
"16515098985",
"182913374493",
"2044565139303",
"23035036108755",
"261312501113193",
"2982280058702499",
"34217698991867058",
"394470188685557271",
"4566935001939261414",
"53076293916648500439",
"618991948535588040078"
]
| [
"nonn"
]
| 13 | 0 | 2 | [
"A356783",
"A380557",
"A382322",
"A382323"
]
| null | Paul D. Hanna, Mar 21 2025 | 2025-03-22T18:50:20 | oeisdata/seq/A382/A382323.seq | d23835df86a31ddd71484e9907c23e57 |
A382324 | a(n) = least integer h >= 1 such that n is a sum of the form Sum_{k>=0} floor(h/m^k) for some integer m >= 2. | [
"1",
"2",
"2",
"3",
"4",
"5",
"4",
"5",
"7",
"6",
"7",
"10",
"9",
"10",
"8",
"9",
"12",
"10",
"11",
"17",
"15",
"12",
"13",
"19",
"14",
"15",
"19",
"20",
"23",
"21",
"16",
"17",
"26",
"18",
"19",
"26",
"29",
"20",
"21",
"27",
"22",
"23",
"33",
"30",
"31",
"24",
"25",
"33",
"26",
"27",
"42",
"40",
"28",
"29",
"38",
"30",
"31",
"40",
"41",
"47",
"42",
"43",
"32",
"33",
"50",
"34",
"35",
"47"
]
| [
"nonn"
]
| 6 | 1 | 2 | [
"A382278",
"A382324"
]
| null | Clark Kimberling, Apr 01 2025 | 2025-04-07T17:52:50 | oeisdata/seq/A382/A382324.seq | 5ca0e1e995b3758d8f5657430e20ff68 |
A382325 | Numbers with a record ratio of proper factorizations to nontrivial divisors. | [
"4",
"16",
"32",
"64",
"128",
"192",
"256",
"384",
"512",
"576",
"768",
"864",
"1024",
"1152",
"1536",
"1728",
"2304",
"3456",
"4608",
"5184",
"5760",
"6912",
"8640",
"9216",
"10368",
"11520",
"13824",
"17280",
"20736",
"23040",
"25920",
"27648",
"34560",
"41472",
"51840",
"62208",
"69120",
"82944",
"103680",
"138240",
"165888",
"172800"
]
| [
"nonn"
]
| 14 | 1 | 1 | [
"A002182",
"A025487",
"A028422",
"A033833",
"A070824",
"A382325",
"A382326",
"A382327"
]
| null | Charles L. Hohn, Mar 21 2025 | 2025-04-02T20:36:56 | oeisdata/seq/A382/A382325.seq | 68296716afad019fcab113d928bbb6ad |
A382326 | Numbers with a record ratio of nontrivial divisors to prime factors (counted with multiplicity). | [
"4",
"6",
"12",
"24",
"30",
"60",
"120",
"180",
"210",
"360",
"420",
"840",
"1260",
"2310",
"2520",
"4620",
"7560",
"9240",
"13860",
"27720",
"55440",
"60060",
"83160",
"110880",
"120120",
"138600",
"166320",
"180180",
"277200",
"360360",
"720720",
"1081080",
"1441440",
"1801800",
"2162160",
"3063060",
"3603600",
"5405400",
"6126120"
]
| [
"nonn"
]
| 14 | 1 | 1 | [
"A001222",
"A002182",
"A025487",
"A070824",
"A382325",
"A382326",
"A382327"
]
| null | Charles L. Hohn, Mar 21 2025 | 2025-04-02T20:37:06 | oeisdata/seq/A382/A382326.seq | e637d6c40ba0202cb88a1feee23aacb3 |
A382327 | Numbers with a record ratio of proper factorizations to prime factors (counted with multiplicity). | [
"4",
"8",
"12",
"24",
"36",
"48",
"60",
"72",
"120",
"144",
"180",
"240",
"288",
"360",
"480",
"576",
"720",
"1080",
"1440",
"2160",
"2520",
"2880",
"3600",
"4320",
"5040",
"7200",
"7560",
"8640",
"10080",
"14400",
"15120",
"20160",
"25200",
"30240",
"40320",
"50400",
"60480",
"80640",
"90720",
"100800",
"120960",
"151200",
"181440",
"201600"
]
| [
"nonn"
]
| 16 | 1 | 1 | [
"A001222",
"A025487",
"A028422",
"A033833",
"A382325",
"A382326",
"A382327"
]
| null | Charles L. Hohn, Mar 21 2025 | 2025-04-02T20:36:51 | oeisdata/seq/A382/A382327.seq | 2f08d00136343d2a20635e1446a268e4 |
A382328 | Maximum possible product of differences of every pair in a set of nonnegative integers with sum n. | [
"1",
"1",
"2",
"3",
"6",
"12",
"20",
"48",
"120",
"240",
"540",
"1440",
"4320",
"11520",
"30240",
"64512",
"207360",
"725760",
"2419200",
"7257600",
"17418240",
"39191040",
"174182400",
"696729600",
"2786918400",
"9405849600",
"25082265600",
"65840947200",
"182891520000",
"1003290624000",
"4514807808000",
"21069103104000"
]
| [
"nonn"
]
| 18 | 0 | 3 | [
"A002620",
"A382328"
]
| null | Zhao Hui Du, Mar 21 2025 | 2025-04-05T18:32:58 | oeisdata/seq/A382/A382328.seq | acb577c5ff562900c50b76e174d5d492 |
A382329 | Least positive integer that gives a square of an integer when multiplied by the n-th harmonic number. | [
"1",
"6",
"66",
"12",
"8220",
"20",
"420",
"213080",
"17965080",
"153720",
"2320468920",
"14109480",
"412970037480",
"422245703880",
"430902992520",
"6076390320",
"516336630329520",
"161488607280",
"21362271268818480",
"866533600973040",
"97555876321904",
"186715152624",
"52866073370045936"
]
| [
"nonn"
]
| 38 | 1 | 2 | [
"A001008",
"A002805",
"A007913",
"A382329"
]
| null | Ali Sada, Mar 21 2025 | 2025-05-11T11:45:41 | oeisdata/seq/A382/A382329.seq | 4a4e50e8b0e7d2dc01c0f315d1bbadbd |
A382330 | a(n) is the number of positive integers k for which Sum_{i=1..j} (p_i+e_i) = n, where p_1^e_1*...*p_j^e_j is the prime factorization of k. | [
"0",
"0",
"1",
"2",
"2",
"3",
"4",
"6",
"8",
"11",
"15",
"21",
"27",
"36",
"47",
"61",
"79",
"104",
"133",
"170",
"215",
"272",
"343",
"433",
"542",
"678",
"845",
"1050",
"1300",
"1608",
"1981",
"2437",
"2988",
"3655",
"4460",
"5433",
"6603",
"8014",
"9705",
"11731",
"14155",
"17055",
"20509",
"24624",
"29512",
"35313",
"42184",
"50315",
"59916",
"71248",
"84598"
]
| [
"nonn"
]
| 11 | 1 | 4 | [
"A008474",
"A219180",
"A377505",
"A377537",
"A382330"
]
| null | Felix Huber, Mar 23 2025 | 2025-03-29T18:38:18 | oeisdata/seq/A382/A382330.seq | 6d92da4718e8e4c8efdc2e1cffac6d27 |
A382331 | If n = Product (p_j^k_j) then a(n) = -Sum ((-1)^k_j * p_j). | [
"0",
"2",
"3",
"-2",
"5",
"5",
"7",
"2",
"-3",
"7",
"11",
"1",
"13",
"9",
"8",
"-2",
"17",
"-1",
"19",
"3",
"10",
"13",
"23",
"5",
"-5",
"15",
"3",
"5",
"29",
"10",
"31",
"2",
"14",
"19",
"12",
"-5",
"37",
"21",
"16",
"7",
"41",
"12",
"43",
"9",
"2",
"25",
"47",
"1",
"-7",
"-3",
"20",
"11",
"53",
"5",
"16",
"9",
"22",
"31",
"59",
"6",
"61",
"33",
"4",
"-2",
"18",
"16",
"67",
"15",
"26",
"14",
"71",
"-1",
"73",
"39",
"-2"
]
| [
"sign",
"easy"
]
| 13 | 1 | 2 | [
"A001414",
"A008472",
"A316523",
"A332422",
"A332423",
"A332424",
"A340901",
"A366749",
"A382331"
]
| null | Ilya Gutkovskiy, Mar 22 2025 | 2025-03-29T18:55:10 | oeisdata/seq/A382/A382331.seq | 493ddb1a7980954dc50b1869fedd219e |
A382332 | Expansion of 1/(1 - 4*x/(1-x)^2)^(7/2). | [
"1",
"14",
"154",
"1470",
"12866",
"106078",
"837018",
"6385262",
"47420674",
"344553902",
"2458367898",
"17272647966",
"119770278978",
"821068784382",
"5572735854234",
"37490757508302",
"250247764120578",
"1658681038111566",
"10924592141535898",
"71541334475749502",
"466060971286552642"
]
| [
"nonn"
]
| 28 | 0 | 2 | [
"A020918",
"A110170",
"A377198",
"A377200",
"A382274",
"A382332"
]
| null | Seiichi Manyama, Mar 30 2025 | 2025-05-12T13:59:52 | oeisdata/seq/A382/A382332.seq | 9dc407c667e972e79c38ae85ad7ed758 |
A382333 | Expansion of ( 1 + 4 * Sum_{k>=0} x^(2^k)/(1 - x^(2^k)) )^(1/2). | [
"1",
"2",
"2",
"-2",
"8",
"-10",
"6",
"26",
"-108",
"258",
"-342",
"-194",
"2700",
"-8994",
"17830",
"-12878",
"-61910",
"322110",
"-860106",
"1284546",
"571880",
"-10749654",
"38883554",
"-82867578",
"68869212",
"286234558",
"-1619591538",
"4559780610",
"-7250287740",
"-2206074398",
"59250601986",
"-225063455922"
]
| [
"sign",
"easy"
]
| 8 | 0 | 2 | [
"A001511",
"A223142",
"A382333",
"A382334",
"A382335"
]
| null | Seiichi Manyama, Mar 22 2025 | 2025-03-22T08:41:26 | oeisdata/seq/A382/A382333.seq | c5579440f2d09b308113ced682d9253e |
A382334 | Expansion of ( 1 + 9 * Sum_{k>=0} x^(2^k)/(1 - x^(2^k)) )^(1/3). | [
"1",
"3",
"-3",
"12",
"-45",
"210",
"-1038",
"5331",
"-28068",
"150645",
"-820713",
"4526157",
"-25217451",
"141722985",
"-802455807",
"4573197111",
"-26211368118",
"150988107936",
"-873651133218",
"5075417681184",
"-29591720994384",
"173094835970280",
"-1015510421231184",
"5973910500301608",
"-35229684687254898"
]
| [
"sign",
"easy"
]
| 9 | 0 | 2 | [
"A001511",
"A223143",
"A382333",
"A382334",
"A382336"
]
| null | Seiichi Manyama, Mar 22 2025 | 2025-03-22T08:41:30 | oeisdata/seq/A382/A382334.seq | 2f1815e86f33e5d7b6ddf9b8e606d4a8 |
A382335 | Expansion of ( 1 + 4 * Sum_{k>=0} x^(2^k)/(1 - x^(2^k))^2 )^(1/2). | [
"1",
"2",
"4",
"-2",
"10",
"-2",
"-20",
"82",
"-108",
"-114",
"1052",
"-2702",
"2054",
"11394",
"-52636",
"99534",
"32938",
"-831698",
"2649676",
"-3119694",
"-8779530",
"54334130",
"-125649628",
"31877726",
"849214460",
"-3274210670",
"5129552132",
"7097067566",
"-65583106070",
"180299051838",
"-133300439300"
]
| [
"sign",
"easy"
]
| 8 | 0 | 2 | [
"A129527",
"A223142",
"A382333",
"A382335",
"A382336"
]
| null | Seiichi Manyama, Mar 22 2025 | 2025-03-22T08:41:49 | oeisdata/seq/A382/A382335.seq | 092966a733fa54eec82119b5d1a398dc |
A382336 | Expansion of ( 1 + 9 * Sum_{k>=0} x^(2^k)/(1 - x^(2^k))^2 )^(1/3). | [
"1",
"3",
"0",
"0",
"21",
"-111",
"504",
"-2004",
"7092",
"-21150",
"43614",
"24288",
"-949878",
"7022118",
"-38308320",
"175670820",
"-691787607",
"2250673143",
"-4994247456",
"-2841846468",
"120496073523",
"-931900270923",
"5282041372722",
"-25033533979260",
"101401747872534",
"-337523450786736",
"757180705527738"
]
| [
"sign",
"easy"
]
| 9 | 0 | 2 | [
"A129527",
"A223143",
"A382334",
"A382335",
"A382336"
]
| null | Seiichi Manyama, Mar 22 2025 | 2025-03-22T08:41:44 | oeisdata/seq/A382/A382336.seq | f4a529989eae9ca417f4db7585c707f2 |
A382337 | Palindromes in base 10 in which the difference between the sums of the digits in the even and odd positions is zero. | [
"0",
"11",
"22",
"33",
"44",
"55",
"66",
"77",
"88",
"99",
"121",
"242",
"363",
"484",
"1001",
"1111",
"1221",
"1331",
"1441",
"1551",
"1661",
"1771",
"1881",
"1991",
"2002",
"2112",
"2222",
"2332",
"2442",
"2552",
"2662",
"2772",
"2882",
"2992",
"3003",
"3113",
"3223",
"3333",
"3443",
"3553",
"3663",
"3773",
"3883",
"3993",
"4004",
"4114",
"4224",
"4334",
"4444",
"4554",
"4664",
"4774",
"4884",
"4994"
]
| [
"nonn",
"easy",
"base"
]
| 28 | 1 | 2 | [
"A002113",
"A135499",
"A382337"
]
| null | Alexander Yutkin, Mar 22 2025 | 2025-03-30T15:23:01 | oeisdata/seq/A382/A382337.seq | d2f32f5ef49a1e508bb053604ef7caef |
A382338 | Positive integers k such that there are at least 3 positive integer solutions (x,y) to the equation x^3 + y^2 = k^2. | [
"105",
"120",
"210",
"260",
"405",
"440",
"504",
"510",
"561",
"665",
"840",
"897",
"960",
"1155",
"1173",
"1485",
"1610",
"1680",
"1947",
"2001",
"2052",
"2080",
"2145",
"2233",
"2415",
"2457",
"2465",
"2628",
"2835",
"2850",
"3045",
"3135",
"3240",
"3300",
"3315",
"3395",
"3520",
"4004",
"4032",
"4080",
"4095",
"4290",
"4488",
"4600",
"4760",
"4950",
"5145",
"5265",
"5320",
"5580",
"5670",
"5795"
]
| [
"nonn"
]
| 21 | 1 | 1 | null | null | Robert Israel, Mar 23 2025 | 2025-04-06T14:54:14 | oeisdata/seq/A382/A382338.seq | 6866d222e1c7cbd97772cef1e9c8dffe |
A382339 | Triangle read by rows: T(n,k) is the number of partitions of a 2-colored set of n objects into exactly k parts with 0 <= k <= n. | [
"1",
"0",
"2",
"0",
"3",
"3",
"0",
"4",
"6",
"4",
"0",
"5",
"14",
"9",
"5",
"0",
"6",
"22",
"24",
"12",
"6",
"0",
"7",
"37",
"49",
"34",
"15",
"7",
"0",
"8",
"52",
"92",
"76",
"44",
"18",
"8",
"0",
"9",
"76",
"157",
"162",
"103",
"54",
"21",
"9",
"0",
"10",
"100",
"260",
"302",
"232",
"130",
"64",
"24",
"10",
"0",
"11",
"135",
"400",
"554",
"468",
"302",
"157",
"74",
"27",
"11"
]
| [
"nonn",
"tabl"
]
| 20 | 0 | 3 | [
"A005380",
"A008284",
"A381891",
"A382339"
]
| null | Peter Dolland, Mar 22 2025 | 2025-04-17T07:03:42 | oeisdata/seq/A382/A382339.seq | 9880f5aa383a35bccfd4df7a7610febd |
A382340 | Triangle read by rows: T(n,k) is the number of partitions of a 3-colored set of n objects into exactly k parts with 0 <= k <= n. | [
"1",
"0",
"3",
"0",
"6",
"6",
"0",
"10",
"18",
"10",
"0",
"15",
"51",
"36",
"15",
"0",
"21",
"105",
"123",
"60",
"21",
"0",
"28",
"208",
"326",
"226",
"90",
"28",
"0",
"36",
"360",
"771",
"678",
"360",
"126",
"36",
"0",
"45",
"606",
"1641",
"1836",
"1161",
"525",
"168",
"45",
"0",
"55",
"946",
"3271",
"4431",
"3403",
"1775",
"721",
"216",
"55",
"0",
"66",
"1446",
"6096",
"10026",
"8982",
"5472",
"2520",
"948",
"270",
"66"
]
| [
"nonn",
"tabl"
]
| 10 | 0 | 3 | [
"A008284",
"A217093",
"A382045",
"A382339",
"A382340"
]
| null | Peter Dolland, Mar 22 2025 | 2025-04-17T07:04:31 | oeisdata/seq/A382/A382340.seq | dc02c28489de1f8e78d840d4d8e98d43 |
A382341 | Triangle read by rows: T(n,k) is the number of partitions of a 4-colored set of n objects into exactly k parts with 0 <= k <= n. | [
"1",
"0",
"4",
"0",
"10",
"10",
"0",
"20",
"40",
"20",
"0",
"35",
"135",
"100",
"35",
"0",
"56",
"340",
"420",
"200",
"56",
"0",
"84",
"784",
"1370",
"950",
"350",
"84",
"0",
"120",
"1596",
"3900",
"3580",
"1800",
"560",
"120",
"0",
"165",
"3070",
"9905",
"11835",
"7425",
"3045",
"840",
"165",
"0",
"220",
"5500",
"23180",
"34780",
"27020",
"13360",
"4760",
"1200",
"220"
]
| [
"nonn",
"tabl"
]
| 12 | 0 | 3 | [
"A008284",
"A255050",
"A382241",
"A382339",
"A382340",
"A382341"
]
| null | Peter Dolland, Mar 22 2025 | 2025-04-17T07:04:54 | oeisdata/seq/A382/A382341.seq | 8fdce2c44038eff4bf65f821d6e48884 |
A382342 | Triangle read by rows: T(n, k) is the number of partitions of n into k parts where 0 <= k <= n, and each part is one of two kinds. | [
"1",
"0",
"2",
"0",
"2",
"3",
"0",
"2",
"4",
"4",
"0",
"2",
"7",
"6",
"5",
"0",
"2",
"8",
"12",
"8",
"6",
"0",
"2",
"11",
"18",
"17",
"10",
"7",
"0",
"2",
"12",
"26",
"28",
"22",
"12",
"8",
"0",
"2",
"15",
"34",
"46",
"38",
"27",
"14",
"9",
"0",
"2",
"16",
"46",
"64",
"66",
"48",
"32",
"16",
"10",
"0",
"2",
"19",
"56",
"94",
"100",
"86",
"58",
"37",
"18",
"11",
"0",
"2",
"20",
"70",
"124",
"152",
"136",
"106",
"68",
"42",
"20",
"12"
]
| [
"nonn",
"tabl"
]
| 22 | 0 | 3 | [
"A000712",
"A008284",
"A022597",
"A381895",
"A382342",
"A382345"
]
| null | Peter Dolland, Mar 27 2025 | 2025-04-19T03:53:53 | oeisdata/seq/A382/A382342.seq | 4bd41f68bc02bbf36276e05fa51dc175 |
A382343 | Triangle read by rows: T(n, k) is the number of partitions of n into k parts where 0 <= k <= n, and each part is one of 3 kinds. | [
"1",
"0",
"3",
"0",
"3",
"6",
"0",
"3",
"9",
"10",
"0",
"3",
"15",
"18",
"15",
"0",
"3",
"18",
"36",
"30",
"21",
"0",
"3",
"24",
"55",
"66",
"45",
"28",
"0",
"3",
"27",
"81",
"114",
"105",
"63",
"36",
"0",
"3",
"33",
"108",
"189",
"195",
"153",
"84",
"45",
"0",
"3",
"36",
"145",
"276",
"348",
"298",
"210",
"108",
"55",
"0",
"3",
"42",
"180",
"405",
"552",
"558",
"423",
"276",
"135",
"66"
]
| [
"nonn",
"tabl"
]
| 12 | 0 | 3 | [
"A000217",
"A000716",
"A008284",
"A022598",
"A382025",
"A382342",
"A382343"
]
| null | Peter Dolland, Mar 27 2025 | 2025-03-28T08:00:03 | oeisdata/seq/A382/A382343.seq | 1e3cd3f1d98b2f54c1ed504f984bd0ab |
A382344 | Triangle read by rows: T(n, k) is the number of partitions of n into k parts where 0 <= k <= n, and each part is one of 4 kinds. | [
"1",
"0",
"4",
"0",
"4",
"10",
"0",
"4",
"16",
"20",
"0",
"4",
"26",
"40",
"35",
"0",
"4",
"32",
"80",
"80",
"56",
"0",
"4",
"42",
"124",
"180",
"140",
"84",
"0",
"4",
"48",
"184",
"320",
"340",
"224",
"120",
"0",
"4",
"58",
"248",
"535",
"660",
"574",
"336",
"165",
"0",
"4",
"64",
"332",
"800",
"1200",
"1184",
"896",
"480",
"220",
"0",
"4",
"74",
"416",
"1176",
"1956",
"2284",
"1932",
"1320",
"660",
"286"
]
| [
"nonn",
"tabl"
]
| 8 | 0 | 3 | [
"A000292",
"A008284",
"A022599",
"A023003",
"A382041",
"A382342",
"A382343",
"A382344"
]
| null | Peter Dolland, Mar 28 2025 | 2025-03-29T04:21:10 | oeisdata/seq/A382/A382344.seq | 0b3ac3a1755af58d758b94eb93491e21 |
A382345 | Square array A(n,k), n>=0, k>=0, read by antidiagonals downwards, where n unlabeled objects are distributed into k containers of two kinds. Containers may be left empty. | [
"1",
"2",
"0",
"3",
"2",
"0",
"4",
"4",
"2",
"0",
"5",
"6",
"7",
"2",
"0",
"6",
"8",
"12",
"8",
"2",
"0",
"7",
"10",
"17",
"18",
"11",
"2",
"0",
"8",
"12",
"22",
"28",
"26",
"12",
"2",
"0",
"9",
"14",
"27",
"38",
"46",
"34",
"15",
"2",
"0",
"10",
"16",
"32",
"48",
"66",
"64",
"46",
"16",
"2",
"0",
"11",
"18",
"37",
"58",
"86",
"100",
"94",
"56",
"19",
"2",
"0",
"12",
"20",
"42",
"68",
"106",
"136",
"152",
"124",
"70",
"20",
"2",
"0"
]
| [
"nonn",
"tabl"
]
| 33 | 0 | 2 | [
"A000712",
"A073252",
"A381895",
"A382342",
"A382345"
]
| null | Peter Dolland, Mar 29 2025 | 2025-04-07T09:26:11 | oeisdata/seq/A382/A382345.seq | fbd4bcda01bb4db634dd08f9fc06f07c |
A382346 | Number of antichains in the Bruhat order on B_n. | [
"3",
"12",
"2247"
]
| [
"nonn",
"hard",
"more",
"bref"
]
| 11 | 1 | 1 | [
"A005900",
"A378072",
"A382346"
]
| null | Dmitry I. Ignatov, May 18 2025 | 2025-05-29T15:46:01 | oeisdata/seq/A382/A382346.seq | c3031cdb571e13cbd9ea255ccd9a4993 |
A382347 | Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = [x^n] Product_{j=0..n} (1 + (k*n+j)*x). | [
"1",
"1",
"1",
"1",
"3",
"2",
"1",
"5",
"26",
"6",
"1",
"7",
"74",
"342",
"24",
"1",
"9",
"146",
"1650",
"5944",
"120",
"1",
"11",
"242",
"4578",
"48504",
"127860",
"720",
"1",
"13",
"362",
"9774",
"189144",
"1763100",
"3272688",
"5040",
"1",
"15",
"506",
"17886",
"520024",
"9660840",
"76223664",
"97053936",
"40320",
"1",
"17",
"674",
"29562",
"1164024",
"34201080",
"586813968",
"3817038960",
"3270729600",
"362880"
]
| [
"nonn",
"tabl"
]
| 20 | 0 | 5 | [
"A000142",
"A165675",
"A380707",
"A382347",
"A382349",
"A383678",
"A384024"
]
| null | Seiichi Manyama, May 18 2025 | 2025-05-18T09:58:24 | oeisdata/seq/A382/A382347.seq | dcd41275b56ed6a77d6180d3167bf2ba |
A382348 | Number of connected bipartite graphs with n edges. | [
"1",
"1",
"2",
"4",
"7",
"17",
"36",
"94",
"237",
"658",
"1845",
"5527",
"16809",
"53357",
"173298",
"580331",
"1988935",
"6991328",
"25124511",
"92325353",
"346401296",
"1326493369"
]
| [
"nonn",
"nice",
"more"
]
| 67 | 1 | 3 | [
"A002905",
"A005142",
"A382348"
]
| null | Sergey Pupyrev, May 29 2025 | 2025-06-09T01:01:37 | oeisdata/seq/A382/A382348.seq | 776903951784d7054718a24b62441de5 |
A382349 | a(n) = [x^n] Product_{k=0..n} (1 + (3*n+k)*x). | [
"1",
"7",
"146",
"4578",
"189144",
"9660840",
"586813968",
"41283943344",
"3299858098560",
"295294500123840",
"29242449106502400",
"3174506423754019200",
"374845813851886709760",
"47828682507084551654400",
"6557612642418946942310400",
"961431335221085133398784000",
"150095351600371197275428454400"
]
| [
"nonn"
]
| 19 | 0 | 2 | [
"A165675",
"A382347",
"A382349"
]
| null | Seiichi Manyama, May 18 2025 | 2025-05-23T03:08:00 | oeisdata/seq/A382/A382349.seq | 55ed2bc20ea50a93c138afc1e4661225 |
A382351 | Numbers with an integer harmonic mean of the indices of distinct prime factors. | [
"2",
"3",
"4",
"5",
"7",
"8",
"9",
"11",
"13",
"16",
"17",
"19",
"23",
"25",
"27",
"29",
"31",
"32",
"37",
"39",
"41",
"43",
"47",
"49",
"53",
"59",
"61",
"64",
"65",
"67",
"71",
"73",
"79",
"81",
"83",
"89",
"97",
"101",
"103",
"107",
"109",
"113",
"117",
"121",
"125",
"127",
"128",
"130",
"131",
"137",
"139",
"149",
"151",
"157",
"163",
"167",
"169",
"173",
"179",
"181",
"191",
"193",
"195",
"197",
"199",
"211"
]
| [
"nonn"
]
| 6 | 1 | 1 | [
"A067340",
"A078174",
"A326621",
"A382351"
]
| null | Ilya Gutkovskiy, Mar 22 2025 | 2025-03-29T18:55:21 | oeisdata/seq/A382/A382351.seq | 76b1d97ab34f7468ac5ff05652371b70 |
A382352 | Numbers k such that the sum of the reciprocals of the indices of distinct prime factors of k is an integer. | [
"1",
"2",
"4",
"8",
"16",
"32",
"64",
"128",
"195",
"256",
"390",
"512",
"585",
"780",
"975",
"1024",
"1170",
"1560",
"1755",
"1950",
"2048",
"2340",
"2535",
"2925",
"3120",
"3510",
"3900",
"4096",
"4680",
"4875",
"5070",
"5265",
"5850",
"6240",
"7020",
"7605",
"7800",
"8192",
"8775",
"9360",
"9750",
"10101",
"10140",
"10530",
"11700",
"12480",
"12675",
"14040",
"14625"
]
| [
"nonn"
]
| 9 | 1 | 2 | [
"A072873",
"A316856",
"A382352"
]
| null | Ilya Gutkovskiy, Mar 22 2025 | 2025-03-29T18:56:54 | oeisdata/seq/A382/A382352.seq | 1bbecb7696df201a3567ef3d650b7fa1 |
A382353 | Numbers k > 0 such that A006218(k) / A018804(k) is an integer. | [
"1",
"2",
"3",
"4",
"8",
"10",
"15",
"43",
"63",
"6934",
"316563",
"2428132",
"56264126"
]
| [
"nonn",
"more"
]
| 13 | 1 | 2 | [
"A006218",
"A018804",
"A382353"
]
| null | Ctibor O. Zizka, Mar 22 2025 | 2025-03-23T08:39:47 | oeisdata/seq/A382/A382353.seq | 02cee63178aec626b44889048650b8e2 |
A382354 | Triangle T(n,k) read by rows, where row n is a permutation of the numbers 1 through n, such that if a deck of n cards is prepared in this order, and under-down-under dealing is used, then the resulting cards will be dealt in increasing order. | [
"1",
"2",
"1",
"3",
"1",
"2",
"2",
"1",
"3",
"4",
"4",
"1",
"5",
"3",
"2",
"4",
"1",
"3",
"5",
"2",
"6",
"3",
"1",
"7",
"5",
"2",
"4",
"6",
"5",
"1",
"7",
"4",
"2",
"8",
"6",
"3",
"7",
"1",
"4",
"6",
"2",
"8",
"5",
"3",
"9",
"4",
"1",
"10",
"8",
"2",
"5",
"7",
"3",
"9",
"6",
"10",
"1",
"7",
"5",
"2",
"11",
"9",
"3",
"6",
"8",
"4",
"9",
"1",
"5",
"11",
"2",
"8",
"6",
"3",
"12",
"10",
"4",
"7",
"5",
"1",
"8",
"10",
"2",
"6",
"12",
"3",
"9",
"7",
"4",
"13",
"11"
]
| [
"nonn",
"tabl"
]
| 10 | 1 | 2 | [
"A006257",
"A225381",
"A321298",
"A378635",
"A382354",
"A382355",
"A382356",
"A382358"
]
| null | Tanya Khovanova, Nathan Sheffield, and the MIT PRIMES STEP junior group, Mar 22 2025 | 2025-04-13T23:20:36 | oeisdata/seq/A382/A382354.seq | 14356108451fa34f0d50c5d086ab40f7 |
A382355 | A version of the Josephus problem: a(n) is the surviving integer under the skip-eliminate-skip version of the elimination process. | [
"1",
"1",
"1",
"4",
"3",
"6",
"3",
"6",
"9",
"3",
"6",
"9",
"12",
"1",
"4",
"7",
"10",
"13",
"16",
"19",
"1",
"4",
"7",
"10",
"13",
"16",
"19",
"22",
"25",
"28",
"31",
"3",
"6",
"9",
"12",
"15",
"18",
"21",
"24",
"27",
"30",
"33",
"36",
"39",
"42",
"45",
"1",
"4",
"7",
"10",
"13",
"16",
"19",
"22",
"25",
"28",
"31",
"34",
"37",
"40",
"43",
"46",
"49",
"52",
"55",
"58",
"61",
"64",
"67",
"70",
"3",
"6"
]
| [
"nonn"
]
| 10 | 1 | 4 | [
"A006257",
"A225381",
"A321298",
"A378635",
"A382354",
"A382355",
"A382356",
"A382358"
]
| null | Tanya Khovanova, Nathan Sheffield, and the MIT PRIMES STEP junior group, Mar 22 2025 | 2025-04-05T23:25:37 | oeisdata/seq/A382/A382355.seq | f17ed0a983a808644186fef5ab480ac2 |
A382356 | Elimination order of the first person in a variation of the Josephus problem, where there are n people total. During each round the first person is skipped, the second is eliminated and the third person is skipped. Then the process repeats. | [
"1",
"2",
"3",
"2",
"4",
"4",
"3",
"5",
"7",
"4",
"10",
"9",
"5",
"14",
"9",
"6",
"10",
"15",
"7",
"18",
"21",
"8",
"19",
"14",
"9",
"15",
"24",
"10",
"21",
"28",
"11",
"23",
"19",
"12",
"20",
"26",
"13",
"31",
"28",
"14",
"36",
"24",
"15",
"25",
"43",
"16",
"47",
"39",
"17",
"44",
"29",
"18",
"30",
"44",
"19",
"40",
"50",
"20",
"42",
"34",
"21",
"35",
"45",
"22",
"57",
"47",
"23",
"55",
"39",
"24"
]
| [
"nonn"
]
| 9 | 1 | 2 | [
"A006257",
"A225381",
"A321298",
"A378635",
"A382354",
"A382355",
"A382356",
"A382358"
]
| null | Tanya Khovanova, Nathan Sheffield, and the MIT PRIMES STEP junior group, Mar 22 2025 | 2025-04-05T23:41:53 | oeisdata/seq/A382/A382356.seq | 361a803cf3cb131606ed0459a16ac6e2 |
A382357 | Lexicographically earliest sequence of distinct positive integers such that the 2-adic valuations of adjacent terms differ exactly by one. | [
"1",
"2",
"3",
"6",
"4",
"8",
"12",
"10",
"5",
"14",
"7",
"18",
"9",
"22",
"11",
"26",
"13",
"30",
"15",
"34",
"17",
"38",
"19",
"42",
"20",
"24",
"16",
"32",
"48",
"40",
"28",
"46",
"21",
"50",
"23",
"54",
"25",
"58",
"27",
"62",
"29",
"66",
"31",
"70",
"33",
"74",
"35",
"78",
"36",
"56",
"44",
"72",
"52",
"82",
"37",
"86",
"39",
"90",
"41",
"94",
"43",
"98",
"45",
"102",
"47",
"106",
"49"
]
| [
"nonn",
"base"
]
| 11 | 1 | 2 | [
"A003602",
"A007814",
"A073675",
"A266089",
"A382357",
"A382360"
]
| null | Rémy Sigrist, Mar 22 2025 | 2025-03-26T16:17:03 | oeisdata/seq/A382/A382357.seq | a8a224cb8301445092c030ae3a7e39fd |
A382358 | Triangle read by rows: T(n,k) is the number of the k-th eliminated person in the variation of the Josephus elimination process for n people, where in each round, the first person is skipped, the second eliminated and the third is skipped. | [
"1",
"2",
"1",
"2",
"3",
"1",
"2",
"1",
"3",
"4",
"2",
"5",
"4",
"1",
"3",
"2",
"5",
"3",
"1",
"4",
"6",
"2",
"5",
"1",
"6",
"4",
"7",
"3",
"2",
"5",
"8",
"4",
"1",
"7",
"3",
"6",
"2",
"5",
"8",
"3",
"7",
"4",
"1",
"6",
"9",
"2",
"5",
"8",
"1",
"6",
"10",
"7",
"4",
"9",
"3",
"2",
"5",
"8",
"11",
"4",
"9",
"3",
"10",
"7",
"1",
"6",
"2",
"5",
"8",
"11",
"3",
"7",
"12",
"6",
"1",
"10",
"4",
"9",
"2",
"5",
"8",
"11",
"1",
"6",
"10",
"3",
"9",
"4",
"13",
"7",
"12"
]
| [
"nonn",
"tabl"
]
| 13 | 1 | 2 | [
"A006257",
"A225381",
"A321298",
"A378635",
"A382354",
"A382355",
"A382356",
"A382358"
]
| null | Tanya Khovanova, Nathan Sheffield, and the MIT PRIMES STEP junior group, Mar 22 2025 | 2025-04-05T23:40:52 | oeisdata/seq/A382/A382358.seq | 3f89fda4633a3d309fe0458c4d2b6e1b |
A382359 | Number of labeled deterministic finite automata with n states and two letters. | [
"2",
"128",
"17496",
"4194304",
"1562500000",
"835884417024",
"607687873272704",
"576460752303423488",
"691636079448571949568",
"1024000000000000000000000",
"1833841138186726138360895488",
"3907429033741066770846918377472",
"9769232732262334599652925506494464"
]
| [
"nonn"
]
| 10 | 1 | 1 | [
"A036289",
"A062206",
"A155957",
"A382359"
]
| null | Anand Jain, Mar 22 2025 | 2025-03-30T15:28:00 | oeisdata/seq/A382/A382359.seq | a6cd77b0ccf6da74bf83b9d8bd81f335 |
A382360 | a(n) is the unique k such that A382357(k) = 2^n. | [
"1",
"2",
"5",
"6",
"27",
"28",
"87",
"88",
"371",
"372",
"1303",
"1304",
"5717",
"5718",
"27099",
"27100",
"100637",
"100638",
"429041",
"429042",
"1676037",
"1676038",
"6566201",
"6566202",
"26703687",
"26703688",
"105939329",
"105939330",
"424972311",
"424972312",
"1688465121",
"1688465122",
"6744826613",
"6744826614"
]
| [
"nonn",
"base"
]
| 6 | 0 | 2 | [
"A382357",
"A382360"
]
| null | Rémy Sigrist, Mar 22 2025 | 2025-03-26T16:16:57 | oeisdata/seq/A382/A382360.seq | 9fa0cd538c3aef37d2123f36c780505b |
A382361 | Number of nonnesting permutations of the multiset {1,1,2,2,...,n,n} that avoid 123. | [
"1",
"4",
"17",
"82",
"406",
"2070",
"10729",
"56394",
"299646",
"1606816",
"8683562"
]
| [
"nonn",
"more"
]
| 43 | 1 | 2 | [
"A177555",
"A382361",
"A383770"
]
| null | Amya Luo, May 26 2025 | 2025-06-17T01:18:18 | oeisdata/seq/A382/A382361.seq | 42587fb0df47d8aa7c461eaf9bc62d45 |
A382362 | Number of oriented Eulerian circuits from a fixed start vertex in the complete digraph K_n, counting distinct first arcs. | [
"1",
"6",
"768",
"3888000",
"1238347284480",
"36133511823360000000",
"132525036775962102988800000000",
"80290170669240213088301154828288000000000",
"10219925826442937385376011199621103616000000000000000000",
"338787616987540767092926393308400759448386388551011812769792000000000000"
]
| [
"nonn",
"walk"
]
| 32 | 2 | 2 | [
"A000272",
"A124355",
"A135388",
"A232545",
"A369820",
"A382362"
]
| null | Florian Ragwitz, Mar 23 2025 | 2025-03-25T19:51:09 | oeisdata/seq/A382/A382362.seq | e8d638497a13af437b1b001a1eb3dcba |
A382363 | Rectangular array read by antidiagonals, T(n,k) is the number of labeled digraphs on [n] along with a (coloring) function c:[n] -> [k] such that for all u,v in [n], u->v implies u<=v and c(u)<=c(v), n>=0, k>=0. | [
"1",
"0",
"1",
"0",
"1",
"1",
"0",
"2",
"2",
"1",
"0",
"8",
"7",
"3",
"1",
"0",
"64",
"44",
"15",
"4",
"1",
"0",
"1024",
"508",
"129",
"26",
"5",
"1",
"0",
"32768",
"10976",
"1962",
"284",
"40",
"6",
"1",
"0",
"2097152",
"450496",
"54036",
"5371",
"530",
"57",
"7",
"1",
"0",
"268435456",
"35535872",
"2747880",
"180424",
"11995",
"888",
"77",
"8",
"1",
"0",
"68719476736",
"5435551744",
"262091808",
"10997576",
"476165",
"23409",
"1379",
"100",
"9",
"1"
]
| [
"nonn",
"tabl"
]
| 29 | 0 | 8 | [
"A006125",
"A382223",
"A382363"
]
| null | Geoffrey Critzer, Mar 23 2025 | 2025-03-24T06:12:39 | oeisdata/seq/A382/A382363.seq | 6357ba9a817abe3ce2acf135f2e9add1 |
A382364 | a(n) is the smallest squarefree number k such that the sum of the digit counts of the prime factors of k equals the sum of n and the digit count of k | [
"6",
"66",
"858",
"72930",
"6374082",
"643782282",
"66309575046"
]
| [
"nonn",
"base",
"more"
]
| 52 | 1 | 1 | [
"A055642",
"A095411",
"A382364"
]
| null | Jean-Marc Rebert, Mar 24 2025 | 2025-04-08T23:29:22 | oeisdata/seq/A382/A382364.seq | 95299ff35d13de19a40381d7e94c920e |
A382365 | Expansion of 1/( 1 - 4 * Sum_{k>=0} x^(2^k) / (1 - x^(2^k)) )^(1/2). | [
"1",
"2",
"10",
"46",
"232",
"1174",
"6078",
"31786",
"167836",
"892258",
"4770466",
"25622286",
"138146540",
"747253022",
"4053224974",
"22038282338",
"120079277626",
"655486778654",
"3584062901182",
"19625809294386",
"107610733877720",
"590751275348362",
"3246588926918074",
"17860031073624694"
]
| [
"nonn"
]
| 8 | 0 | 2 | [
"A327736",
"A382187",
"A382365",
"A382366"
]
| null | Seiichi Manyama, Mar 22 2025 | 2025-03-23T10:08:26 | oeisdata/seq/A382/A382365.seq | b99e5700667b91b0d8388a7ce150dd31 |
A382366 | Expansion of 1/( 1 - 9 * Sum_{k>=0} x^(2^k) / (1 - x^(2^k)) )^(1/3). | [
"1",
"3",
"24",
"201",
"1818",
"17004",
"163068",
"1590798",
"15718899",
"156860076",
"1577644998",
"15969030780",
"162498057048",
"1660951840611",
"17042090466264",
"175436835017475",
"1811209862304735",
"18746380864328061",
"194465530800628908",
"2021343414865754583",
"21048513676138546848"
]
| [
"nonn"
]
| 8 | 0 | 2 | [
"A327736",
"A382188",
"A382365",
"A382366"
]
| null | Seiichi Manyama, Mar 22 2025 | 2025-03-23T10:08:22 | oeisdata/seq/A382/A382366.seq | df4587af38248644632f55e65fb0a447 |
A382367 | Expansion of 1/( 1 - Sum_{k>=0} x^(3^k) / (1 - x^(3^k)) ). | [
"1",
"1",
"2",
"5",
"10",
"21",
"46",
"97",
"206",
"442",
"940",
"2002",
"4272",
"9103",
"19400",
"41360",
"88156",
"187901",
"400534",
"853747",
"1819782",
"3878965",
"8268160",
"17623888",
"37566072",
"80073580",
"170680002",
"363811370",
"775478548",
"1652963605",
"3523358532",
"7510180375",
"16008251264",
"34122231512"
]
| [
"nonn"
]
| 11 | 0 | 3 | [
"A051064",
"A327736",
"A382367",
"A382368",
"A382369",
"A382372",
"A382373",
"A382378"
]
| null | Seiichi Manyama, Mar 22 2025 | 2025-03-23T10:08:18 | oeisdata/seq/A382/A382367.seq | 55adb4d6d72daeab93ea2fe495dc7bcb |
A382368 | Expansion of 1/( 1 - 4 * Sum_{k>=0} x^(3^k) / (1 - x^(3^k)) )^(1/2). | [
"1",
"2",
"8",
"36",
"162",
"750",
"3536",
"16858",
"81100",
"392914",
"1914268",
"9369190",
"46032396",
"226898158",
"1121510176",
"5556731592",
"27589816042",
"137240945530",
"683808343416",
"3412128301538",
"17048743841882",
"85286538527304",
"427112389604968",
"2141096012912290",
"10743017708448232"
]
| [
"nonn"
]
| 7 | 0 | 2 | [
"A382367",
"A382368",
"A382369"
]
| null | Seiichi Manyama, Mar 22 2025 | 2025-03-23T10:08:13 | oeisdata/seq/A382/A382368.seq | 97e5237b9c241f7cc9f0daa6c5a24dba |
A382369 | Expansion of 1/( 1 - 9 * Sum_{k>=0} x^(3^k) / (1 - x^(3^k)) )^(1/3). | [
"1",
"3",
"21",
"168",
"1416",
"12396",
"111219",
"1015221",
"9386643",
"87650775",
"824926152",
"7813623234",
"74403686022",
"711670543635",
"6833183666862",
"65826593737206",
"635962416394296",
"6159757277793783",
"59796182640515031",
"581643107427461664",
"5667929195670139296",
"55322424966010598556"
]
| [
"nonn"
]
| 8 | 0 | 2 | [
"A382367",
"A382368",
"A382369"
]
| null | Seiichi Manyama, Mar 22 2025 | 2025-03-23T10:08:09 | oeisdata/seq/A382/A382369.seq | cd332ce099938b75bc8dc8e782f543a9 |
A382370 | Numbers k such that (k - 1)^(k + 1) - k is prime. | [
"3",
"4",
"5",
"7",
"10",
"11",
"21",
"46",
"59",
"839",
"21920"
]
| [
"nonn",
"more"
]
| 18 | 1 | 1 | [
"A238378",
"A240532",
"A382370"
]
| null | Juri-Stepan Gerasimov, Mar 23 2025 | 2025-04-05T16:40:45 | oeisdata/seq/A382/A382370.seq | 4d750f13b3d904b84e0484ec4cc660f0 |
A382371 | Remove all occurrences of a digit from n such that the resulting number, formed by the remaining digits in their original order, is as large as possible. If no digits remain, a(n)=0. | [
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"2",
"2",
"0",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"3",
"3",
"3",
"0",
"4",
"5",
"6",
"7",
"8",
"9",
"4",
"4",
"4",
"4",
"0",
"5",
"6",
"7",
"8",
"9",
"5",
"5",
"5",
"5",
"5",
"0",
"6",
"7",
"8",
"9",
"6",
"6",
"6",
"6",
"6",
"6",
"0",
"7",
"8",
"9",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"0",
"8",
"9",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8"
]
| [
"nonn",
"base",
"look"
]
| 12 | 1 | 12 | [
"A010785",
"A382102",
"A382371"
]
| null | Rémy Sigrist, Mar 23 2025 | 2025-03-23T23:22:39 | oeisdata/seq/A382/A382371.seq | 5ead58ffced734a88759289cf8fdfa00 |
A382372 | Expansion of 1/( 1 - Sum_{k>=0} x^(4^k) / (1 - x^(4^k)) ). | [
"1",
"1",
"2",
"4",
"9",
"18",
"37",
"76",
"158",
"325",
"670",
"1381",
"2850",
"5876",
"12117",
"24986",
"51530",
"106262",
"219131",
"451885",
"931876",
"1921695",
"3962884",
"8172182",
"16852538",
"34752996",
"71667001",
"147790386",
"304770689",
"628492615",
"1296066140",
"2672724207",
"5511643710",
"11366012289"
]
| [
"nonn"
]
| 13 | 0 | 3 | [
"A115362",
"A327736",
"A382367",
"A382372",
"A382373",
"A382378"
]
| null | Seiichi Manyama, Mar 23 2025 | 2025-03-23T10:08:05 | oeisdata/seq/A382/A382372.seq | 505344931cf62480581d920f4b13929a |
A382373 | Expansion of 1/( 1 - Sum_{k>=0} x^(5^k) / (1 - x^(5^k)) ). | [
"1",
"1",
"2",
"4",
"8",
"17",
"34",
"69",
"140",
"284",
"578",
"1173",
"2382",
"4837",
"9822",
"19948",
"40508",
"82261",
"167050",
"339233",
"688896",
"1398964",
"2840926",
"5769169",
"11715654",
"23791402",
"48314044",
"98113049",
"199241660",
"404607125",
"821650100",
"1668554099",
"3388392198",
"6880928638",
"13973346686"
]
| [
"nonn"
]
| 9 | 0 | 3 | [
"A055457",
"A327736",
"A382367",
"A382372",
"A382373",
"A382378"
]
| null | Seiichi Manyama, Mar 23 2025 | 2025-03-23T10:08:01 | oeisdata/seq/A382/A382373.seq | 9b5051d25915d966c67bf31f06ed1858 |
A382374 | Lexicographically earliest sequence of distinct positive integers such that the number of prime factors counted with multiplicity of adjacent terms differ exactly by one. | [
"1",
"2",
"4",
"3",
"6",
"5",
"9",
"7",
"10",
"8",
"14",
"11",
"15",
"12",
"16",
"18",
"21",
"13",
"22",
"17",
"25",
"19",
"26",
"20",
"24",
"27",
"33",
"23",
"34",
"28",
"35",
"29",
"38",
"30",
"36",
"32",
"40",
"42",
"39",
"31",
"46",
"37",
"49",
"41",
"51",
"43",
"55",
"44",
"54",
"45",
"56",
"48",
"60",
"50",
"57",
"47",
"58",
"52",
"62",
"53",
"65",
"59",
"69",
"61",
"74",
"63",
"77"
]
| [
"nonn"
]
| 11 | 1 | 2 | [
"A001222",
"A382229",
"A382357",
"A382374",
"A382375",
"A382376"
]
| null | Rémy Sigrist, Mar 23 2025 | 2025-03-26T18:19:42 | oeisdata/seq/A382/A382374.seq | 2df6463255a6033f28f29d76fe9915c7 |
A382375 | Lexicographically earliest sequence of distinct positive integers such that the number of prime factors counted with multiplicity of n and a(n) differ exactly by one. | [
"2",
"1",
"4",
"3",
"6",
"5",
"9",
"10",
"7",
"8",
"14",
"15",
"21",
"11",
"12",
"18",
"22",
"16",
"25",
"24",
"13",
"17",
"26",
"20",
"19",
"23",
"33",
"34",
"35",
"36",
"38",
"40",
"27",
"28",
"29",
"30",
"39",
"31",
"37",
"32",
"46",
"49",
"51",
"54",
"55",
"41",
"57",
"56",
"42",
"58",
"43",
"60",
"62",
"44",
"45",
"48",
"47",
"50",
"65",
"52",
"69",
"53",
"74",
"72",
"59",
"77",
"82"
]
| [
"nonn"
]
| 11 | 1 | 1 | [
"A001222",
"A382374",
"A382375",
"A382377"
]
| null | Rémy Sigrist, Mar 23 2025 | 2025-03-26T20:56:04 | oeisdata/seq/A382/A382375.seq | cd7928aa0262d604d32e1866efe88113 |
A382376 | Lexicographically earliest sequence of distinct positive integers such that the number of distinct prime factors of adjacent terms differ exactly by one. | [
"1",
"2",
"6",
"3",
"10",
"4",
"12",
"5",
"14",
"7",
"15",
"8",
"18",
"9",
"20",
"11",
"21",
"13",
"22",
"16",
"24",
"17",
"26",
"19",
"28",
"23",
"33",
"25",
"34",
"27",
"35",
"29",
"36",
"30",
"38",
"31",
"39",
"32",
"40",
"37",
"44",
"41",
"45",
"42",
"46",
"43",
"48",
"47",
"50",
"49",
"51",
"53",
"52",
"59",
"54",
"60",
"55",
"61",
"56",
"64",
"57",
"66",
"58",
"67",
"62",
"70",
"63"
]
| [
"nonn"
]
| 12 | 1 | 2 | [
"A001221",
"A382357",
"A382374",
"A382376",
"A382377"
]
| null | Rémy Sigrist, Mar 23 2025 | 2025-03-26T17:49:13 | oeisdata/seq/A382/A382376.seq | 9c4804551098d496741c73e50e65f7ba |
A382377 | Lexicographically earliest sequence of distinct positive integers such that the number of distinct prime factors of n and a(n) differ exactly by one. | [
"2",
"1",
"6",
"10",
"12",
"3",
"14",
"15",
"18",
"4",
"20",
"5",
"21",
"7",
"8",
"22",
"24",
"9",
"26",
"11",
"13",
"16",
"28",
"17",
"33",
"19",
"34",
"23",
"35",
"36",
"38",
"39",
"25",
"27",
"29",
"30",
"40",
"31",
"32",
"37",
"44",
"45",
"46",
"41",
"42",
"43",
"48",
"47",
"50",
"49",
"53",
"59",
"51",
"60",
"61",
"64",
"66",
"67",
"52",
"54",
"55",
"70",
"71",
"56",
"73",
"57",
"58"
]
| [
"nonn"
]
| 12 | 1 | 1 | [
"A001221",
"A382375",
"A382376",
"A382377"
]
| null | Rémy Sigrist, Mar 23 2025 | 2025-03-26T17:49:09 | oeisdata/seq/A382/A382377.seq | 2021af161550acfd62e11b5a26cc572d |
A382378 | Expansion of 1/( 1 - Sum_{k>=0} x^(6^k) / (1 - x^(6^k)) ). | [
"1",
"1",
"2",
"4",
"8",
"16",
"33",
"66",
"133",
"268",
"540",
"1088",
"2194",
"4421",
"8910",
"17957",
"36190",
"72936",
"146996",
"296252",
"597061",
"1203306",
"2425121",
"4887544",
"9850272",
"19852060",
"40009486",
"80634401",
"162509126",
"327517977",
"660073866",
"1330301036",
"2681064864",
"5403370072",
"10889855193",
"21947218962"
]
| [
"nonn"
]
| 8 | 0 | 3 | [
"A122841",
"A327736",
"A373216",
"A382367",
"A382372",
"A382373",
"A382378"
]
| null | Seiichi Manyama, Mar 23 2025 | 2025-03-23T10:07:57 | oeisdata/seq/A382/A382378.seq | d72f88666fa96ffd016820e52c06d00d |
A382379 | Table read by rows: row n is the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 is A000032(n) and such that its long leg and its hypotenuse are consecutive natural numbers. | [
"3",
"4",
"5",
"1",
"0",
"1",
"5",
"12",
"13",
"7",
"24",
"25",
"13",
"84",
"85",
"21",
"220",
"221",
"35",
"612",
"613",
"57",
"1624",
"1625",
"93",
"4324",
"4325",
"151",
"11400",
"11401",
"245",
"30012",
"30013",
"397",
"78804",
"78805",
"643",
"206724",
"206725",
"1041",
"541840",
"541841",
"1685",
"1419612",
"1419613",
"2727",
"3718264",
"3718265"
]
| [
"nonn",
"easy",
"tabf"
]
| 20 | 0 | 1 | [
"A000032",
"A382379",
"A382409",
"A382410"
]
| null | Miguel-Ángel Pérez García-Ortega, Mar 24 2025 | 2025-03-31T01:59:10 | oeisdata/seq/A382/A382379.seq | 49198f7bdf5c275b6284f0024edbc014 |
A382380 | Greater of twin self numbers, i.e., larger member of the pair of self numbers differing by 2. | [
"3",
"5",
"7",
"9",
"110",
"211",
"312",
"413",
"514",
"615",
"716",
"817",
"918",
"1111",
"1212",
"1313",
"1414",
"1515",
"1616",
"1717",
"1818",
"1919",
"2112",
"2213",
"2314",
"2415",
"2516",
"2617",
"2718",
"2819",
"2920",
"3113",
"3214",
"3315",
"3416",
"3517",
"3618",
"3719",
"3820",
"3921",
"4114",
"4215",
"4316",
"4417",
"4518",
"4619",
"4720",
"4821",
"4922",
"5115",
"5216",
"5317",
"5418"
]
| [
"nonn",
"base"
]
| 16 | 1 | 1 | [
"A003052",
"A374101",
"A382380"
]
| null | Shyam Sunder Gupta, Mar 23 2025 | 2025-04-25T20:40:41 | oeisdata/seq/A382/A382380.seq | cfb0909bcd15e09031360523e6438477 |
A382381 | Lexicographically earliest sequence of distinct positive integers such that any two subsets with at least two terms have distinct variances. | [
"1",
"2",
"4",
"8",
"16",
"25",
"36",
"62",
"136",
"320",
"411",
"1208",
"1295",
"4179",
"5143",
"6380",
"31370",
"34425",
"36094",
"213044",
"218759",
"306722"
]
| [
"nonn",
"hard",
"more"
]
| 20 | 1 | 2 | [
"A138857",
"A260873",
"A381856",
"A382381",
"A382382",
"A382383"
]
| null | Pontus von Brömssen, Mar 23 2025 | 2025-04-07T17:46:47 | oeisdata/seq/A382/A382381.seq | 6a63e4d80cd29ef6f5625a5b26998766 |
A382382 | Least k for which there exists an n-subset X of {0, ..., k} such that the variances of the subsets of X of size at least 2 are distinct. | [
"0",
"1",
"3",
"6",
"11",
"17",
"27",
"48"
]
| [
"nonn",
"more"
]
| 9 | 1 | 3 | [
"A003022",
"A382381",
"A382382",
"A382383"
]
| null | Pontus von Brömssen, Mar 23 2025 | 2025-03-29T15:31:49 | oeisdata/seq/A382/A382382.seq | 5522d70a8b273ea224afe88a02b84a0e |
A382383 | Number of distinct variances of nonempty subsets of {1, ..., n}. | [
"0",
"1",
"2",
"4",
"7",
"13",
"23",
"40",
"68",
"124",
"208",
"368",
"559",
"918",
"1352",
"2017",
"2891",
"4122",
"5506",
"7458",
"9623",
"12620",
"16125",
"20626",
"25401",
"31513",
"38587",
"47244",
"56592",
"68021",
"80503",
"95859",
"112137",
"131986",
"153353",
"178434",
"205627",
"236266",
"269884",
"307167",
"346844",
"394924",
"445797",
"501739"
]
| [
"nonn"
]
| 23 | 0 | 3 | [
"A005418",
"A135342",
"A208531",
"A382381",
"A382382",
"A382383"
]
| null | Pontus von Brömssen, Mar 23 2025 | 2025-04-06T06:37:33 | oeisdata/seq/A382/A382383.seq | 6f7ffa59ab1ce33b11bb41b31ed390c0 |
A382384 | Number of minimum connected dominating sets in the n-Goldberg graph. | [
"6",
"96",
"290",
"744",
"1974",
"5376",
"15642",
"45480",
"124014",
"343008",
"944658",
"2596776",
"7116390",
"19409664",
"52694730",
"142812648",
"385840030",
"1039911520",
"2796034626",
"7501233256",
"20084164374",
"53677896192",
"143214557050",
"381504047912",
"1014784646094",
"2695617288672",
"7151420301682"
]
| [
"nonn",
"easy"
]
| 17 | 3 | 1 | [
"A004767",
"A382384",
"A382431"
]
| null | Eric W. Weisstein, Mar 23 2025 | 2025-06-04T09:52:19 | oeisdata/seq/A382/A382384.seq | 8122ab297d7bb66e01b6ff742652070b |
A382385 | Number of minimum dominating sets in the n X n fiveleaper graph. | [
"1",
"1",
"1",
"1",
"1",
"112",
"12",
"32",
"4809",
"48",
"860",
"9840",
"2"
]
| [
"nonn",
"more"
]
| 20 | 1 | 6 | null | null | Eric W. Weisstein, Mar 23 2025 | 2025-06-01T09:58:09 | oeisdata/seq/A382/A382385.seq | f7be5adb8df683349c277ac1a7667edb |
A382386 | Number of minimum dominating sets in the n X n giraffe graph. | [
"1",
"1",
"1",
"1",
"56",
"172",
"14",
"152",
"18",
"56",
"2",
"192",
"224",
"4340",
"2016",
"352",
"8"
]
| [
"nonn",
"more"
]
| 29 | 1 | 5 | null | null | Eric W. Weisstein, Mar 23 2025 | 2025-06-25T14:44:12 | oeisdata/seq/A382/A382386.seq | 362e14f227c1f0a4336b40d34bc08724 |
A382387 | Number of minimum dominating sets in the n X n zebra graph. | [
"1",
"1",
"1",
"1",
"448",
"28",
"552",
"25",
"1588",
"1028",
"6",
"656",
"40"
]
| [
"nonn",
"more"
]
| 23 | 1 | 5 | null | null | Eric W. Weisstein, Mar 23 2025 | 2025-06-21T16:16:50 | oeisdata/seq/A382/A382387.seq | fa0bff2baaae99bc46b5214bbef2299f |
A382388 | Number of minimum dominating sets in the n X n antelope graph. | [
"1",
"1",
"1",
"1",
"1",
"81",
"1344",
"32"
]
| [
"nonn",
"more"
]
| 16 | 1 | 6 | null | null | Eric W. Weisstein, Mar 23 2025 | 2025-03-30T09:52:24 | oeisdata/seq/A382/A382388.seq | 7f00ebe7e170c2bf1cd038e9c5b7e246 |
A382389 | Numbers k such that k, prime(k) and primepi(reverse(prime(k))) are emirps (A006567). | [
"7673",
"9001",
"12491",
"17749",
"31481",
"75041",
"93887",
"95881",
"102061",
"104479",
"112621",
"113557",
"118429",
"139999",
"722713",
"743891",
"749927",
"999133",
"1001941",
"1086353",
"1115071",
"1165511",
"1233907",
"1861913",
"1861973",
"1881697",
"1927903",
"1972259"
]
| [
"nonn",
"base"
]
| 6 | 1 | 1 | [
"A006567",
"A382389"
]
| null | Ivan N. Ianakiev, Mar 23 2025 | 2025-03-27T10:13:52 | oeisdata/seq/A382/A382389.seq | 54f2dee648fcafc20d6f090812730a8f |
A382390 | Number of minimum dominating sets in the n X n camel graph. | [
"1",
"1",
"1",
"9",
"92",
"4",
"4",
"16",
"48",
"576"
]
| [
"nonn",
"more"
]
| 10 | 1 | 4 | null | null | Eric W. Weisstein, Mar 23 2025 | 2025-03-23T17:01:53 | oeisdata/seq/A382/A382390.seq | 52fb1b3fc715661432a40a31970ba337 |
A382391 | Numbers k such that (23^k - 3^k)/20 is prime. | [
"3",
"7",
"31",
"47",
"109",
"151",
"223",
"463",
"739",
"6427",
"17581",
"30517"
]
| [
"nonn",
"hard",
"more"
]
| 5 | 1 | 1 | [
"A062587",
"A062589",
"A127996",
"A127997",
"A128344",
"A204940",
"A217320",
"A225807",
"A229542",
"A375161",
"A375236",
"A377031",
"A382391"
]
| null | Robert Price, Mar 23 2025 | 2025-03-23T12:53:28 | oeisdata/seq/A382/A382391.seq | 798d7a988353dd62e2826e913408826b |
A382392 | a(n) is the least prime number whose factorial base expansion contains the digit n. | [
"2",
"2",
"5",
"19",
"97",
"601",
"4327",
"35281",
"322571",
"3265949",
"36288017",
"439084817",
"5748019201",
"80951270459",
"1220496076831",
"19615115520037",
"334764638208037",
"6046686277632071",
"115242726703104073",
"2311256907767808001",
"48658040163532800037",
"1072909785605898240031"
]
| [
"nonn",
"base"
]
| 7 | 0 | 1 | [
"A001563",
"A062584",
"A090703",
"A382392"
]
| null | Rémy Sigrist, Mar 23 2025 | 2025-03-24T15:14:57 | oeisdata/seq/A382/A382392.seq | f4f3aa49935d772f96147e5153deb8a7 |
A382393 | Positive integers k such that 6*k - 1 is prime for k != 1 (mod 5) and (6*k - 1)/5 is prime for k == 1 (mod 5). | [
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"11",
"12",
"14",
"15",
"16",
"17",
"18",
"19",
"22",
"23",
"25",
"26",
"28",
"29",
"30",
"31",
"32",
"33",
"36",
"38",
"39",
"40",
"42",
"43",
"44",
"45",
"47",
"49",
"51",
"52",
"53",
"56",
"58",
"59",
"60",
"61",
"64",
"65",
"66",
"67",
"70",
"72",
"74",
"75",
"77",
"78",
"80",
"81",
"82",
"84",
"85",
"86",
"87",
"91",
"93",
"94",
"95",
"98",
"99",
"100"
]
| [
"nonn"
]
| 10 | 1 | 1 | [
"A024898",
"A024899",
"A382393"
]
| null | V. Barbera, Mar 23 2025 | 2025-03-30T16:26:14 | oeisdata/seq/A382/A382393.seq | 73498a8e8d7fd3c689e8a9d312044890 |
A382394 | a(n) = Sum_{k=0..n} A128899(n,k)^3. | [
"1",
"1",
"9",
"190",
"5705",
"204876",
"8209278",
"354331692",
"16140234825",
"765868074400",
"37525317999884",
"1886768082651816",
"96906387191038334",
"5066711735118128200",
"268954195756648761900",
"14464077426547576156440",
"786729115199980286001225",
"43219452658242723841261800"
]
| [
"nonn"
]
| 24 | 0 | 3 | [
"A001700",
"A003161",
"A024492",
"A088218",
"A128899",
"A183069",
"A382394"
]
| null | Seiichi Manyama, Mar 24 2025 | 2025-03-24T10:21:57 | oeisdata/seq/A382/A382394.seq | aba92305a487f21c90bb2f4df870f682 |
A382395 | Number of maximum sized subsets of {1..n} such that every pair of distinct elements has a different difference. | [
"1",
"1",
"1",
"3",
"2",
"6",
"14",
"2",
"10",
"26",
"60",
"110",
"4",
"22",
"68",
"156",
"320",
"584",
"8",
"24",
"80",
"206",
"504",
"1004",
"1910",
"3380",
"10",
"34",
"98",
"282",
"760",
"1618",
"3334",
"6360",
"11482",
"2",
"22",
"70",
"214",
"540",
"1250",
"2718",
"5712",
"10910",
"20418",
"2",
"12",
"30",
"90",
"230",
"562",
"1228",
"2690",
"5550",
"11260",
"21164",
"2",
"4",
"6",
"10",
"18"
]
| [
"nonn"
]
| 10 | 0 | 4 | [
"A143823",
"A143824",
"A325879",
"A377410",
"A382395",
"A382396",
"A382398"
]
| null | Andrew Howroyd, Mar 23 2025 | 2025-03-24T15:15:13 | oeisdata/seq/A382/A382395.seq | 7e8dac18ca1659a3989411cbd6400820 |
A382396 | Number of minimum sized maximal subsets of {1..n} such that every pair of distinct elements has a different difference. | [
"1",
"1",
"1",
"3",
"1",
"6",
"14",
"18",
"14",
"10",
"4",
"110",
"172",
"216",
"226",
"214",
"184",
"152",
"116",
"82",
"50",
"26",
"10",
"3696",
"3904",
"3942",
"3768",
"3504",
"3016",
"2548",
"2060",
"1598",
"1170",
"832",
"538",
"330",
"196",
"106",
"52",
"20",
"10",
"4",
"2",
"69610",
"62594",
"55294",
"47610",
"40502",
"33538",
"27254",
"21544",
"16764",
"12676",
"9258",
"6534",
"4516",
"3042",
"1990",
"1254",
"754",
"448"
]
| [
"nonn"
]
| 8 | 0 | 4 | [
"A143823",
"A325879",
"A377419",
"A382395",
"A382396",
"A382397"
]
| null | Andrew Howroyd, Mar 23 2025 | 2025-03-24T15:15:09 | oeisdata/seq/A382/A382396.seq | a9d3a1770ea163ddde288a7fa49684c1 |
A382397 | Minimum size of a maximal subset of {1..n} such that every pair of distinct elements has a different difference. | [
"0",
"1",
"2",
"2",
"2",
"3",
"3",
"3",
"3",
"3",
"3",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"4",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"5",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6",
"6"
]
| [
"nonn",
"more"
]
| 8 | 0 | 3 | [
"A143824",
"A325879",
"A377419",
"A382396",
"A382397"
]
| null | Andrew Howroyd, Mar 23 2025 | 2025-03-24T15:15:04 | oeisdata/seq/A382/A382397.seq | 056b3d49694c964d004da269911beb29 |
A382398 | Number of maximum sized subsets of {1..n} such that every pair of distinct elements has a different sum. | [
"1",
"1",
"1",
"1",
"4",
"2",
"8",
"22",
"2",
"14",
"40",
"102",
"214",
"4",
"24",
"92",
"236",
"564",
"1148",
"4",
"18",
"90",
"270",
"694",
"1558",
"2",
"6",
"24",
"76",
"252",
"632",
"1554",
"3282",
"6820",
"12942",
"6",
"24",
"84",
"246",
"664",
"1562",
"3442",
"7084",
"14336",
"27202",
"50520",
"2",
"26",
"88",
"294",
"704",
"1716",
"3708",
"8028",
"16108",
"31466",
"58320",
"107136",
"4",
"20",
"54"
]
| [
"nonn"
]
| 6 | 0 | 5 | [
"A039836",
"A196723",
"A325878",
"A382395",
"A382398"
]
| null | Andrew Howroyd, Mar 23 2025 | 2025-03-24T15:15:17 | oeisdata/seq/A382/A382398.seq | 695d768bce68940efc844fe67152c5e2 |
A382399 | Number of subsets of Z_n such that every ordered pair of distinct elements has a different difference. | [
"1",
"2",
"3",
"7",
"9",
"16",
"19",
"43",
"49",
"100",
"91",
"177",
"193",
"352",
"323",
"691",
"673",
"1242",
"1135",
"2129",
"2041",
"3634",
"3103",
"5843",
"5473",
"9326",
"8139",
"16579",
"14001",
"24796",
"21271",
"38813",
"34369",
"60292",
"49539",
"86451",
"81361",
"131684",
"110391",
"196717",
"171761",
"286878",
"236167",
"419337",
"370569",
"618346",
"501999",
"872415",
"763777",
"1235438",
"1028451"
]
| [
"nonn"
]
| 12 | 0 | 2 | [
"A143823",
"A325679",
"A325681",
"A382399",
"A382400"
]
| null | Andrew Howroyd, Mar 24 2025 | 2025-03-27T18:33:31 | oeisdata/seq/A382/A382399.seq | 4fd5ec0c7e4d0b9e1d0858d2537f84c8 |
A382400 | Number of subsets of Z_n such that every ordered pair of distinct elements has a different sum. | [
"1",
"2",
"4",
"8",
"15",
"26",
"48",
"78",
"133",
"202",
"316",
"474",
"755",
"1054",
"1604",
"2196",
"3305",
"4370",
"6208",
"8228",
"11631",
"15086",
"20912",
"26842",
"37581",
"46626",
"64052",
"79984",
"109635",
"133314",
"176156",
"217094",
"291409",
"343872",
"457828",
"547576",
"718375",
"852074",
"1112128",
"1308230",
"1714741"
]
| [
"nonn"
]
| 6 | 0 | 2 | [
"A000125",
"A196723",
"A382399",
"A382400"
]
| null | Andrew Howroyd, Mar 27 2025 | 2025-03-27T18:33:24 | oeisdata/seq/A382/A382400.seq | 259245e6bec8a53c7832ce680d876994 |
A382401 | a(n) is the number formed by removing all copies of the smallest digit of n, or 0 if no digits remain. | [
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"2",
"2",
"0",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"3",
"3",
"3",
"0",
"4",
"5",
"6",
"7",
"8",
"9",
"4",
"4",
"4",
"4",
"0",
"5",
"6",
"7",
"8",
"9",
"5",
"5",
"5",
"5",
"5",
"0",
"6",
"7",
"8",
"9",
"6",
"6",
"6",
"6",
"6",
"6",
"0",
"7",
"8",
"9",
"7",
"7",
"7",
"7",
"7",
"7",
"7",
"0",
"8",
"9",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"8",
"0",
"9",
"9",
"9",
"9",
"9",
"9",
"9",
"9",
"9",
"9",
"0",
"1",
"11",
"12",
"13",
"14",
"15",
"16",
"17",
"18",
"19",
"11",
"0",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"12"
]
| [
"nonn",
"base",
"look"
]
| 22 | 1 | 12 | [
"A054054",
"A382056",
"A382371",
"A382401"
]
| null | Paolo Xausa, Mar 23 2025 | 2025-03-24T05:57:32 | oeisdata/seq/A382/A382401.seq | 5df139c5127d443f18a0fc3d6093053a |
A382402 | Numbers divisible by the product of their digits (mod 10). | [
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"11",
"12",
"15",
"24",
"26",
"34",
"35",
"37",
"48",
"55",
"62",
"64",
"66",
"72",
"73",
"75",
"76",
"78",
"84",
"88",
"95",
"96",
"98",
"99",
"111",
"112",
"115",
"126",
"132",
"134",
"135",
"136",
"137",
"144",
"148",
"155",
"162",
"164",
"168",
"172",
"173",
"175",
"176",
"184",
"188",
"192",
"195",
"196",
"198",
"199",
"212",
"216",
"228",
"232",
"244",
"248",
"264",
"266"
]
| [
"nonn",
"base"
]
| 19 | 1 | 2 | [
"A007602",
"A064700",
"A371281",
"A382402"
]
| null | Enrique Navarrete, Mar 23 2025 | 2025-06-02T08:29:19 | oeisdata/seq/A382/A382402.seq | d882f97c33d3d662fa2127e88b985c3f |
A382403 | a(n) = Sum_{k=0..n} A039599(n,k)^3. | [
"1",
"2",
"36",
"980",
"33040",
"1268568",
"53105976",
"2364239592",
"110206067400",
"5323547715200",
"264576141331216",
"13458185494436592",
"697931136204820336",
"36789784967375728400",
"1966572261077797609200",
"106400946932857148590800",
"5817987630644593688220600",
"321105713814359742307398480"
]
| [
"nonn"
]
| 11 | 0 | 2 | [
"A000984",
"A039599",
"A048990",
"A112029",
"A382403"
]
| null | Seiichi Manyama, Mar 24 2025 | 2025-03-24T10:22:02 | oeisdata/seq/A382/A382403.seq | 2c7cf39def2ef27972e2f19383764af6 |
A382404 | a(n) = -Sum_{k=0..n} (-1)^k * A039599(n,k)^3. | [
"-1",
"0",
"18",
"480",
"11550",
"275184",
"6597360",
"159629184",
"3897563670",
"95946708000",
"2378998624860",
"59359563244800",
"1489281975509328",
"37545821365718400",
"950601539891016000",
"24159023128878865920",
"616066120184552310150",
"15757649689979967739200"
]
| [
"sign"
]
| 7 | 0 | 3 | [
"A039599",
"A382404"
]
| null | Seiichi Manyama, Mar 24 2025 | 2025-03-24T10:22:06 | oeisdata/seq/A382/A382404.seq | e2756f980e52ee9ceb082fe89d85afaf |
A382405 | a(n) = Sum_{k=0..n} binomial(n,k)^2 * binomial(n+k,k) * 2^(n-k). | [
"1",
"4",
"34",
"352",
"4006",
"48184",
"600916",
"7687936",
"100240198",
"1326277144",
"17753591164",
"239915864896",
"3267780399196",
"44805617380528",
"617844108170344",
"8561667414341632",
"119151750609504838",
"1664497333624420888",
"23330380347342383404",
"327990673915214512192",
"4623496960858710060916"
]
| [
"nonn",
"easy"
]
| 24 | 0 | 2 | [
"A001850",
"A005258",
"A069835",
"A274671",
"A382405",
"A382642",
"A382848"
]
| null | Ilya Gutkovskiy, Apr 08 2025 | 2025-06-22T00:16:14 | oeisdata/seq/A382/A382405.seq | cb3b69adebeb0cd30194c16d9339127d |
A382406 | Expansion of 1/(1 - x*(1 + x)^2)^3. | [
"1",
"3",
"12",
"37",
"111",
"315",
"864",
"2307",
"6027",
"15471",
"39132",
"97755",
"241606",
"591636",
"1437078",
"3465748",
"8305161",
"19788957",
"46910232",
"110686101",
"260064912",
"608684490",
"1419591546",
"3300027546",
"7648265728",
"17676484410",
"40747630332",
"93704299336",
"214999206831",
"492262973433"
]
| [
"nonn",
"easy"
]
| 60 | 0 | 2 | [
"A000217",
"A001628",
"A002478",
"A362126",
"A382406",
"A382614"
]
| null | Seiichi Manyama, Mar 31 2025 | 2025-04-10T10:46:39 | oeisdata/seq/A382/A382406.seq | 716db09feab607b2730dea0f1cd3e81a |
A382407 | a(n) is the number of partitions n = x + y + z of positive integers such that x*y + y*z + x*z is a perfect square. | [
"0",
"0",
"0",
"0",
"0",
"1",
"1",
"0",
"0",
"0",
"1",
"1",
"0",
"3",
"0",
"1",
"1",
"1",
"2",
"2",
"2",
"1",
"1",
"1",
"1",
"3",
"0",
"5",
"1",
"1",
"2",
"3",
"3",
"2",
"1",
"1",
"3",
"6",
"1",
"4",
"2",
"7",
"4",
"4",
"0",
"3",
"5",
"3",
"4",
"2",
"1",
"7",
"2",
"1",
"5",
"9",
"3",
"5",
"3",
"4",
"1",
"9",
"2",
"6",
"3",
"5",
"6",
"5",
"4",
"7",
"5",
"1",
"5",
"6",
"3",
"13",
"7",
"8",
"4",
"6",
"0",
"4",
"4",
"11",
"5",
"13",
"2"
]
| [
"nonn"
]
| 6 | 1 | 14 | [
"A000244",
"A005030",
"A066955",
"A069905",
"A338939",
"A375512",
"A375576",
"A375580",
"A375731",
"A382407"
]
| null | Felix Huber, Apr 04 2025 | 2025-04-10T21:13:21 | oeisdata/seq/A382/A382407.seq | 51edd7d6e686b758d3494c8f78190a17 |
A382408 | a(n) is the number of terms in A071174 whose radical is A144338(n). | [
"1",
"1",
"1",
"5",
"1",
"9",
"1",
"1",
"13",
"14",
"1",
"1",
"20",
"21",
"1",
"25",
"1",
"406",
"1",
"32",
"33",
"34",
"1",
"37",
"38",
"1",
"820",
"1",
"45",
"1",
"50",
"1",
"54",
"56",
"57",
"1",
"1",
"61",
"64",
"2080",
"1",
"68",
"2346",
"1",
"1",
"73",
"76",
"2926",
"1",
"81",
"1",
"84",
"85",
"86",
"1",
"90",
"92",
"93",
"94",
"1",
"1",
"5050",
"1",
"5356",
"105",
"1",
"1",
"5886",
"110"
]
| [
"nonn"
]
| 11 | 1 | 4 | [
"A007947",
"A071174",
"A144338",
"A382408"
]
| null | Felix Huber, Apr 04 2025 | 2025-04-26T03:33:06 | oeisdata/seq/A382/A382408.seq | f5dc5e16f516211558c9785e3467c6d8 |
A382409 | Semiperimeter of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 is A000032(n) and such that its long leg and its hypotenuse are consecutive natural numbers. | [
"6",
"1",
"15",
"28",
"91",
"231",
"630",
"1653",
"4371",
"11476",
"30135",
"79003",
"207046",
"542361",
"1420455",
"3719628",
"9739491",
"25500511",
"66764790",
"174798253",
"457637131",
"1198124676",
"3136755615",
"8212172403",
"21499810566",
"56287338481",
"147362333055",
"385799868028",
"1010037606571",
"2644313494551",
"6922903755510"
]
| [
"nonn",
"easy"
]
| 11 | 0 | 1 | [
"A000032",
"A382379",
"A382409",
"A382410"
]
| null | Miguel-Ángel Pérez García-Ortega, Mar 24 2025 | 2025-03-30T18:13:07 | oeisdata/seq/A382/A382409.seq | c6b985e03ff5c7ae296a48476a8d9ff3 |
A382410 | Area of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 is A000032(n) and such that its long leg and its hypotenuse are consecutive natural numbers. | [
"6",
"0",
"30",
"84",
"546",
"2310",
"10710",
"46284",
"201066",
"860700",
"3676470",
"15642594",
"66461766",
"282027720",
"1196023110",
"5069852964",
"21485317146",
"91036824270",
"385700191830",
"1634014069044",
"6922219243506",
"29324101445100",
"124221795865230",
"526219583239434",
"2229121859293446",
"9442763903572560"
]
| [
"nonn",
"easy"
]
| 9 | 0 | 1 | [
"A000032",
"A382379",
"A382409",
"A382410"
]
| null | Miguel-Ángel Pérez García-Ortega, Mar 24 2025 | 2025-03-30T18:13:31 | oeisdata/seq/A382/A382410.seq | 96cb86b52c92ce54155d7d43fc700e32 |
A382411 | a(n) is the greatest possible length of a circular sequence on n symbols such that: no two adjacent symbols are the same, any group of n adjacent symbols contains at least n-1 different symbols, and all groups of n adjacent symbols within the sequence are unique. | [
"1",
"2",
"12",
"96",
"840",
"7920",
"80640",
"887040",
"10523520",
"134265600",
"1836172800",
"26824089600",
"417210393600",
"6887085004800",
"120306041856000",
"2217815728128000",
"43038178799616000",
"877125197684736000",
"18733345462960128000",
"418459145406382080000",
"9758369954796503040000",
"237164153561075220480000"
]
| [
"nonn",
"easy"
]
| 27 | 1 | 2 | [
"A000142",
"A152947",
"A382411"
]
| null | Dean D. Ballard, Mar 24 2025 | 2025-04-08T13:20:11 | oeisdata/seq/A382/A382411.seq | 6eca51a0e0cd89010c7c6c685edb4ba1 |
A382412 | Numbers with no zeros in their base-7 representation. | [
"1",
"2",
"3",
"4",
"5",
"6",
"8",
"9",
"10",
"11",
"12",
"13",
"15",
"16",
"17",
"18",
"19",
"20",
"22",
"23",
"24",
"25",
"26",
"27",
"29",
"30",
"31",
"32",
"33",
"34",
"36",
"37",
"38",
"39",
"40",
"41",
"43",
"44",
"45",
"46",
"47",
"48",
"57",
"58",
"59",
"60",
"61",
"62",
"64",
"65",
"66",
"67",
"68",
"69",
"71",
"72",
"73",
"74",
"75",
"76",
"78",
"79",
"80",
"81",
"82",
"83",
"85",
"86",
"87",
"88",
"89",
"90"
]
| [
"nonn",
"base",
"easy"
]
| 8 | 1 | 2 | [
"A007093",
"A023705",
"A023721",
"A032924",
"A043393",
"A052382",
"A126646",
"A248910",
"A249102",
"A255805",
"A255808",
"A382412",
"A382413"
]
| null | Paolo Xausa, Mar 24 2025 | 2025-03-26T21:48:43 | oeisdata/seq/A382/A382412.seq | 0d045db4aaba666e931336f7cba79522 |
A382413 | Numbers with at least one zero in their base-7 representation. | [
"0",
"7",
"14",
"21",
"28",
"35",
"42",
"49",
"50",
"51",
"52",
"53",
"54",
"55",
"56",
"63",
"70",
"77",
"84",
"91",
"98",
"99",
"100",
"101",
"102",
"103",
"104",
"105",
"112",
"119",
"126",
"133",
"140",
"147",
"148",
"149",
"150",
"151",
"152",
"153",
"154",
"161",
"168",
"175",
"182",
"189",
"196",
"197",
"198",
"199",
"200",
"201",
"202",
"203",
"210",
"217",
"224",
"231",
"238"
]
| [
"nonn",
"base",
"easy"
]
| 8 | 1 | 2 | [
"A007093",
"A011540",
"A043393",
"A062289",
"A081605",
"A196032",
"A382412",
"A382413",
"A382415",
"A382416",
"A382417",
"A382418"
]
| null | Paolo Xausa, Mar 24 2025 | 2025-03-26T21:48:50 | oeisdata/seq/A382/A382413.seq | 965dbf8e9bc5a6a75a7f9de5ec3b95e0 |
A382414 | Primes p such that gcd(ord_p(2), ord_p(5)) = 1. | [
"31",
"601",
"2593",
"599479",
"204700049",
"466344409",
"668731841",
"11638603429"
]
| [
"nonn",
"hard",
"more"
]
| 56 | 1 | 1 | [
"A014664",
"A211241",
"A344202",
"A382414",
"A383411"
]
| null | Li GAN, Apr 26 2025 | 2025-05-03T14:22:49 | oeisdata/seq/A382/A382414.seq | ed6f88057d2e336d721d528fbec3ea16 |
A382415 | Numbers with at least one zero in their base-5 representation. | [
"0",
"5",
"10",
"15",
"20",
"25",
"26",
"27",
"28",
"29",
"30",
"35",
"40",
"45",
"50",
"51",
"52",
"53",
"54",
"55",
"60",
"65",
"70",
"75",
"76",
"77",
"78",
"79",
"80",
"85",
"90",
"95",
"100",
"101",
"102",
"103",
"104",
"105",
"110",
"115",
"120",
"125",
"126",
"127",
"128",
"129",
"130",
"131",
"132",
"133",
"134",
"135",
"136",
"137",
"138",
"139",
"140",
"141",
"142",
"143",
"144",
"145"
]
| [
"nonn",
"base",
"easy"
]
| 7 | 1 | 2 | [
"A007091",
"A011540",
"A023721",
"A023722",
"A062289",
"A081605",
"A196032",
"A382413",
"A382415",
"A382416",
"A382417",
"A382418"
]
| null | Paolo Xausa, Mar 25 2025 | 2025-03-26T21:49:01 | oeisdata/seq/A382/A382415.seq | a8a55e2253f3afcb7b9d717a421f7fc0 |
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