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1999-12-11 03:00:00
2025-04-28 00:58:08
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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", "new" ]
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
d5793456c1a7e0a85af33ed354aac1d5
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", "changed" ]
30
1
1
[ "A003617", "A382899", "A382981" ]
null
Jean-Marc Rebert, Apr 08 2025
2025-04-16T09:02:08
oeisdata/seq/A382/A382899.seq
0aa9e05de0b2daa7e8109945714ed40e
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" ]
4
0
2
[ "A239120", "A382907" ]
null
Sean A. Irvine, Apr 08 2025
2025-04-08T19:33:56
oeisdata/seq/A382/A382907.seq
4aab44855285296aacf918d028232a0b
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", "new" ]
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
cd732fb681187e2e3567280bdf988f8d
A382909
Number of possible (area, dinv) interchanging bijections of Dyck paths of length 2n.
[ "1", "1", "1", "1", "16", "165112971264", "7081067777179913483347996561235301491807900639024696524800000000000000000000" ]
[ "nonn", "new" ]
24
1
5
null
null
Blake Jackson, Apr 08 2025
2025-04-19T06:16:50
oeisdata/seq/A382/A382909.seq
5befd9056c439e8e75c3eeb302b91834
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", "new" ]
28
0
4
[ "A000045", "A003266", "A007598", "A090281", "A382910" ]
null
Edwin Hermann, Apr 08 2025
2025-04-15T15:42:45
oeisdata/seq/A382/A382910.seq
f417418a1fe70c264ec9c147764d4eba
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", "new" ]
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
3c3869179e90fd0d05eac616c39fda7f
A382912
Numbers k such that row k of A305936 (a multiset whose multiplicities are the prime indices of k) is a Look-and-Say partition, meaning it has a 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", "new" ]
12
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
2025-04-18T14:29:23
oeisdata/seq/A382/A382912.seq
383428dcc0665b5d82623f480a31218d
A382913
Numbers k such that row k of A305936 (a multiset whose multiplicities are the prime indices of k) is not a Look-and-Say partition, meaning it has no 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", "new" ]
12
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
2025-04-18T14:29:18
oeisdata/seq/A382/A382913.seq
ad029ae6acecba3361d3d25f229d0f5e
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", "changed" ]
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
4f32a95d5626c5d094a06a238bc97ad5
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
A382917
G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)^3 / (1-x)^3 ).
[ "1", "1", "7", "52", "432", "3878", "36694", "360498", "3642534", "37613947", "395204413", "4211469308", "45409525116", "494500127617", "5430864937915", "60083846523038", "669005596426438", "7491245872785003", "84305386452532885", "953020276395635246", "10816782722212619970", "123218274878407738497" ]
[ "nonn" ]
10
0
3
[ "A349331", "A382916", "A382917", "A382921" ]
null
Seiichi Manyama, Apr 08 2025
2025-04-09T07:28:35
oeisdata/seq/A382/A382917.seq
558c1f55eb25485f9b2e3e1d34638e08
A382918
G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x) / (1-x)^2 )^2.
[ "1", "2", "11", "64", "401", "2652", "18241", "129216", "936469", "6911238", "51764834", "392494366", "3006851913", "23238830982", "180974578418", "1418728452902", "11186978492689", "88668723061112", "706042492550773", "5645331629000370", "45307653034905824", "364860349786846894", "2947299389835541583" ]
[ "nonn" ]
11
0
2
[ "A006319", "A366176", "A382918", "A382920" ]
null
Seiichi Manyama, Apr 08 2025
2025-04-09T07:28:23
oeisdata/seq/A382/A382918.seq
cfed00daaebfe7baa9086d381e4234e1
A382919
G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x) / (1-x)^3 )^2.
[ "1", "2", "13", "84", "580", "4216", "31824", "247168", "1962800", "15866016", "130122304", "1080101760", "9057113472", "76610188544", "652895283200", "5600752756224", "48323092761344", "419068973537792", "3650909105378304", "31937405800724480", "280419948474447872", "2470473454986891264" ]
[ "nonn" ]
12
0
2
[ "A213282", "A360100", "A382616", "A382919", "A382921" ]
null
Seiichi Manyama, Apr 08 2025
2025-04-09T07:28:48
oeisdata/seq/A382/A382919.seq
709ba99a24398506c50bfc5f105f932f
A382920
G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x) / (1-x)^2 )^3.
[ "1", "3", "21", "160", "1320", "11511", "104451", "976317", "9337182", "90937403", "898861308", "8994246132", "90932043400", "927452701605", "9531607969788", "98609173435172", "1026121044859890", "10733030463200814", "112783955395845926", "1190060614961391945", "12604133970419399208", "133945684546835994915" ]
[ "nonn" ]
10
0
2
[ "A006319", "A382916", "A382918", "A382920" ]
null
Seiichi Manyama, Apr 08 2025
2025-04-09T14:16:14
oeisdata/seq/A382/A382920.seq
54c44f35ee5cf0a6407c41dd8f6b4ee0
A382921
G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x) / (1-x)^3 )^3.
[ "1", "3", "24", "199", "1776", "16713", "163429", "1644852", "16929576", "177384877", "1885842105", "20292695751", "220595817213", "2418988309494", "26726104358958", "297226167487469", "3324654200094495", "37379224636055040", "422182501323170275", "4788001977121735326", "54502930562354983641" ]
[ "nonn" ]
11
0
2
[ "A360100", "A382615", "A382917", "A382919", "A382921" ]
null
Seiichi Manyama, Apr 08 2025
2025-04-09T07:29:09
oeisdata/seq/A382/A382921.seq
1dd6d94cb82aeec1f36fa88fd16fad66
A382922
Numbers k such that Fibonacci(k) is a Smith number.
[ "31", "77", "231", "354", "523", "535", "631", "819", "827", "830", "991", "1234" ]
[ "nonn", "base", "more" ]
18
1
1
[ "A000045", "A006753", "A382922" ]
null
Shyam Sunder Gupta, Apr 08 2025
2025-04-13T16:15:45
oeisdata/seq/A382/A382922.seq
1440c8492c70c69cc5a5393c6bdd9356
A382923
Square array A(n,k), n >= 0, k >= 0, read by downward antidiagonals: A(n,k) is the number of m-compositions of n with k zeros.
[ "1", "0", "1", "0", "2", "3", "0", "3", "5", "7", "0", "4", "13", "16", "16", "0", "5", "14", "33", "40", "35", "0", "6", "29", "70", "105", "100", "75", "0", "7", "27", "88", "207", "292", "244", "159", "0", "8", "51", "152", "336", "604", "758", "576", "334", "0", "9", "44", "206", "588", "1161", "1749", "1920", "1329", "696", "0", "10", "79", "300", "882", "2076", "3685", "4924", "4802", "3028", "1442" ]
[ "nonn", "easy", "tabl", "changed" ]
15
0
5
[ "A038207", "A101509", "A181331", "A261780", "A323429", "A382923", "A382924" ]
null
John Tyler Rascoe, Apr 09 2025
2025-04-14T07:39:26
oeisdata/seq/A382/A382923.seq
509ccf9ab9c773ac41a2634d9f2070a6
A382924
Number of m-compositions of n with n zeros.
[ "1", "2", "13", "70", "336", "2076", "11091", "65210", "365661", "2159354", "11713047", "71427504", "392916687", "2245186352", "13527678851", "73679458270", "429472428457", "2553994191220", "14264421153074", "80483620074092", "489077890675807", "2768919905996888", "15394229582049408", "91794448088043258" ]
[ "nonn" ]
10
0
2
[ "A038207", "A101509", "A181331", "A261780", "A323429", "A382820", "A382923", "A382924" ]
null
John Tyler Rascoe, Apr 09 2025
2025-04-10T02:49:48
oeisdata/seq/A382/A382924.seq
785843b9c412ba7cefa70fc5717e5138
A382927
Smallest beginning of a sequence of exactly n consecutive palindromic primes, all ending with the same digit.
[ "2", "181", "151", "131", "101", "11", "17471", "16661", "16561", "16361", "16061", "15551", "15451", "14741", "14341", "13931", "13831", "13331", "12821", "12721", "12421", "11411", "11311", "10601", "10501", "10301", "1884881", "1883881", "1881881", "1880881", "1879781", "1878781", "1876781", "1865681", "1856581", "1853581", "1851581" ]
[ "nonn", "base", "new" ]
48
1
1
[ "A002385", "A054681", "A382927" ]
null
Jean-Marc Rebert, Apr 13 2025
2025-04-19T16:45:04
oeisdata/seq/A382/A382927.seq
8c80eba391c175decd5e2bcb238bb1bd
A382928
Start with {1, x}, then at each step replace it with the set of all pairwise products and sums of its elements (an element can be paired with itself). a(n) gives the number of elements after n-th step.
[ "2", "6", "28", "436", "90385", "4017112742" ]
[ "nonn", "more", "hard" ]
28
0
1
[ "A352969", "A382928" ]
null
Bryle Morga, Apr 09 2025
2025-04-11T16:19:54
oeisdata/seq/A382/A382928.seq
ab9ae75923c6a3ad74862883672f5fa2
A382929
Smallest number k such that k + n + sigma(n) is a perfect number.
[ "4", "1", "21", "17", "17", "10", "13", "5", "6", "0", "5", "456", "1", "458", "457", "449", "461", "439", "457", "434", "443", "438", "449", "412", "440", "428", "429", "412", "437", "394", "433", "401", "415", "408", "413", "369", "421", "398", "401", "366", "413", "358", "409", "368", "373", "378", "401", "324", "390", "353", "373", "346", "389", "322", "369", "320", "359", "348", "377", "268" ]
[ "nonn" ]
57
1
1
[ "A000396", "A155085", "A382506", "A382929" ]
null
Leo Hennig, Apr 09 2025
2025-04-11T16:25:03
oeisdata/seq/A382/A382929.seq
8006ca084ff8b7fd964d8dc9b75e2b2e
A382930
a(n) is the smallest k such that A382506(k) + sigma(k) = A000396(n).
[ "1", "4", "16", "180", "2520", "7207200" ]
[ "nonn", "more", "new" ]
24
1
2
[ "A002093", "A002182", "A382506", "A382930" ]
null
Leo Hennig, Apr 09 2025
2025-04-24T23:25:03
oeisdata/seq/A382/A382930.seq
99958dedf9f6560c964c510acb288418
A382931
Numbers k for which the Pythagorean triangle (A046083(k), A046084(k), A009000(k)) has an integer altitude.
[ "7", "19", "36", "51", "69", "88", "99", "106", "126", "147", "163", "187", "196", "208", "227", "240", "250", "273", "293", "314", "342", "361", "384", "392", "409", "434", "455", "459", "483", "504", "507", "525", "549", "552", "579", "599", "627", "649", "679", "702", "711", "718", "724", "744", "752", "775", "802", "829", "854", "879", "894", "908", "935", "960" ]
[ "nonn", "new" ]
9
1
1
[ "A009000", "A046083", "A046084", "A382931", "A382932" ]
null
Felix Huber, Apr 11 2025
2025-04-19T17:48:30
oeisdata/seq/A382/A382931.seq
140d6c509534d5b2324d81d48735c3ee
A382932
a(n) is the altitude of the Pythagorean triangle (A046083(A382931(n)), A046084(A382931(n)), A009000(A382931(n))).
[ "12", "24", "36", "48", "60", "72", "60", "84", "96", "108", "120", "132", "120", "144", "156", "120", "168", "180", "192", "204", "216", "228", "240", "180", "252", "264", "276", "240", "288", "300", "168", "312", "324", "240", "336", "348", "360", "372", "384", "396", "420", "300", "408", "360", "420", "432", "444", "456", "468", "480", "360", "492", "504", "516" ]
[ "nonn", "new" ]
11
1
1
[ "A008594", "A009000", "A046083", "A046084", "A382931", "A382932" ]
null
Felix Huber, Apr 13 2025
2025-04-19T17:49:02
oeisdata/seq/A382/A382932.seq
d343382a1522638f5ab62bfc61185d33
A382933
Numbers k such that k, 2*m +- 3 and 3*m +- 2 are all semiprimes.
[ "451", "707", "871", "1313", "1537", "1819", "1921", "1969", "2155", "2195", "2533", "2599", "2885", "2993", "3265", "3817", "3883", "3953", "3997", "4069", "4105", "4385", "4555", "4607", "5599", "5755", "5771", "6155", "6415", "6773", "7157", "7453", "7979", "8185", "8213", "8251", "8321", "8333", "8399", "8531", "9055", "9077", "9167", "9335", "9647", "9953", "9977", "10121", "10537" ]
[ "nonn", "new" ]
13
1
1
[ "A001358", "A382933" ]
null
Zak Seidov and Robert Israel, Apr 15 2025
2025-04-17T09:51:25
oeisdata/seq/A382/A382933.seq
75705947a28a19cf7b981d26ab5e7d30
A382934
a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n+k,k) * binomial(n+2*k,k) * 2^(n-k).
[ "1", "8", "142", "3188", "79306", "2091128", "57251944", "1609275536", "46123258714", "1341870616928", "39505611952852", "1174352843125976", "35189447673190864", "1061579548438995776", "32210037668484980992", "982173609216589910528", "30079350892561552670554", "924711257106480733093616", "28524228913983070512002044" ]
[ "nonn", "changed" ]
10
0
2
[ "A001850", "A069835", "A081798", "A126086", "A382934" ]
null
Ilya Gutkovskiy, Apr 09 2025
2025-04-17T04:28:38
oeisdata/seq/A382/A382934.seq
132a8fb8b5e1cdb0f2284247bbc60cc7
A382935
Lexicographically earliest sequence of distinct nonnegative integers such that if a digit d in the digit stream (ignoring commas) is odd, the previous digit is > d.
[ "0", "2", "1", "4", "3", "6", "5", "8", "7", "10", "20", "21", "22", "12", "14", "16", "18", "24", "26", "28", "30", "40", "41", "42", "43", "44", "31", "46", "32", "48", "34", "36", "38", "50", "60", "61", "62", "63", "64", "65", "66", "51", "68", "52", "80", "81", "82", "83", "84", "85", "86", "53", "87", "54", "88", "56", "58", "70", "200", "202", "100", "204", "102", "104", "106", "108", "71", "206", "120", "208" ]
[ "nonn", "base", "look", "new" ]
14
1
2
[ "A342042", "A342043", "A342044", "A342045", "A382462", "A382621", "A382935", "A382936", "A382937", "A382938" ]
null
Paolo Xausa, Apr 14 2025
2025-04-17T09:41:44
oeisdata/seq/A382/A382935.seq
ba8a39bfa39ad34a5f12cd5ba83aa8dc
A382936
First differences of A382935.
[ "2", "-1", "3", "-1", "3", "-1", "3", "-1", "3", "10", "1", "1", "-10", "2", "2", "2", "6", "2", "2", "2", "10", "1", "1", "1", "1", "-13", "15", "-14", "16", "-14", "2", "2", "12", "10", "1", "1", "1", "1", "1", "1", "-15", "17", "-16", "28", "1", "1", "1", "1", "1", "1", "-33", "34", "-33", "34", "-32", "2", "12", "130", "2", "-102", "104", "-102", "2", "2", "2", "-37", "135", "-86", "88", "-136" ]
[ "sign", "base", "new" ]
5
1
1
[ "A382935", "A382936" ]
null
Paolo Xausa, Apr 14 2025
2025-04-17T09:46:01
oeisdata/seq/A382/A382936.seq
38dab52289d3239248e18128016886a4
A382937
Positive integers that contain an odd digit d immediately preceded by a digit <= d.
[ "11", "13", "15", "17", "19", "23", "25", "27", "29", "33", "35", "37", "39", "45", "47", "49", "55", "57", "59", "67", "69", "77", "79", "89", "99", "101", "103", "105", "107", "109", "110", "111", "112", "113", "114", "115", "116", "117", "118", "119", "123", "125", "127", "129", "130", "131", "132", "133", "134", "135", "136", "137", "138", "139", "145", "147", "149", "150" ]
[ "nonn", "base", "easy", "new" ]
11
1
1
[ "A347298", "A382464", "A382623", "A382937", "A382938" ]
null
Paolo Xausa, Apr 14 2025
2025-04-21T10:46:05
oeisdata/seq/A382/A382937.seq
a0191d664aaa62c86a94ce450f8013b3
A382938
Nonnegative integers such that every odd digit except the leftmost is immediately preceded by a larger digit.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "12", "14", "16", "18", "20", "21", "22", "24", "26", "28", "30", "31", "32", "34", "36", "38", "40", "41", "42", "43", "44", "46", "48", "50", "51", "52", "53", "54", "56", "58", "60", "61", "62", "63", "64", "65", "66", "68", "70", "71", "72", "73", "74", "75", "76", "78", "80", "81", "82", "83", "84", "85", "86", "87", "88", "90", "91", "92", "93", "94", "95" ]
[ "nonn", "base", "easy", "new" ]
14
1
3
[ "A377912", "A382465", "A382624", "A382937", "A382938" ]
null
Paolo Xausa, Apr 14 2025
2025-04-21T10:46:01
oeisdata/seq/A382/A382938.seq
2ac093f6a8493ec6a6519beb48cfdcd8
A382939
Split A382935 into runs of increasing elements. a(n) is the length of the n-th run.
[ "2", "2", "2", "2", "5", "13", "2", "2", "11", "2", "8", "2", "2", "5", "2", "4", "2", "2", "4", "4", "3", "2", "5", "3", "5", "6", "3", "2", "7", "30", "2", "5", "4", "5", "2", "5", "5", "2", "5", "2", "5", "6", "2", "2", "10", "2", "2", "2", "19", "2", "5", "4", "6", "2", "8", "2", "7", "2", "9", "2", "8", "2", "10", "2", "2", "5", "2", "7", "2", "6", "2", "6", "2", "9", "2", "7", "2", "8", "2", "12", "10", "4", "4", "3", "2", "4", "3" ]
[ "nonn", "base", "new" ]
6
1
1
[ "A382935", "A382939" ]
null
Paolo Xausa, Apr 14 2025
2025-04-17T09:46:41
oeisdata/seq/A382/A382939.seq
995259fab740c92964b543d3694681bb
A382945
a(n) is the least positive integer k having a divisor d such that k/d is not a power of n and the base n expansions of k and d, possibly with leading zeros, have, up to order, the same digits.
[ "9", "28", "18", "16", "40", "36", "42", "64", "105", "45", "154", "105", "130", "168", "260", "120", "340", "96", "266", "275", "495", "231", "460", "351", "450", "273", "792", "175", "928", "280", "682", "1024", "308", "459", "1302", "741", "962", "665", "1612", "288", "1804", "560", "1290", "1265", "2139", "1035", "1974", "540", "952", "715", "2720", "585" ]
[ "nonn", "base", "new" ]
13
2
1
[ "A096092", "A382945", "A382946" ]
null
Rémy Sigrist, Apr 09 2025
2025-04-14T09:07:52
oeisdata/seq/A382/A382945.seq
dfbe8009f38540c057d052eaeb8ad66e
A382946
a(n) is the least positive integer k having a proper divisor d such that the base n expansions of k and d, without leading zeros, have, up to order, the same digits, or a(n) = -1 if no such k exists.
[ "-1", "64", "36", "16", "700", "36", "42", "64", "3105", "45", "594", "105", "130", "168", "945", "120", "1666", "96", "266", "275", "2457", "231", "460", "351", "450", "273", "7938", "175", "7714", "280", "682", "1024", "308", "459", "7525", "741", "962", "665", "27300", "288", "17097", "560", "1290", "1265", "18540", "1035", "1974", "540", "952", "715" ]
[ "sign", "base", "new" ]
11
2
2
[ "A023094", "A090056", "A382945", "A382946" ]
null
Rémy Sigrist, Apr 09 2025
2025-04-14T09:07:47
oeisdata/seq/A382/A382946.seq
ac29d90871d7be82d8c658e929185d1d
A382947
a(n) = [(x*y)^n] Product_{k>=1} 1 / (1 - x^k - y^k)^k.
[ "1", "2", "16", "78", "426", "1940", "9300", "40530", "177940", "749788", "3137352", "12865488", "52425432", "211336062", "848099898", "3385259588", "13475690578", "53504526568", "212146065506", "840218845230", "3325872415258", "13159945010474", "52064974607244", "205979887425498", "814961759722486" ]
[ "nonn" ]
12
0
2
[ "A000219", "A322211", "A382947" ]
null
Ilya Gutkovskiy, Apr 09 2025
2025-04-11T10:38:18
oeisdata/seq/A382/A382947.seq
bf647fe2ae14c25505e26d0976903c16
A382948
a(n) = [(x*y)^n] Product_{k>=1} (1 + x^k + y^k)^k.
[ "1", "0", "2", "18", "50", "190", "536", "1644", "4432", "12876", "33560", "89118", "227734", "572578", "1409602", "3424996", "8150818", "19152532", "44455758", "101565172", "229712612", "513207144", "1134650028", "2481664146", "5379539720", "11545719858", "24574548632", "51855844492", "108559596182" ]
[ "nonn" ]
9
0
3
[ "A026007", "A365662", "A382948" ]
null
Ilya Gutkovskiy, Apr 09 2025
2025-04-11T10:22:39
oeisdata/seq/A382/A382948.seq
9d16a45157b608a948daacd6e45e9640
A382949
a(n) = [(x*y)^n] Product_{k>=1} 1 / (1 - x^k - y^k)^n.
[ "1", "2", "48", "1190", "33648", "996292", "30626316", "965163166", "30995087312", "1009925740946", "33289934968618", "1107728567917028", "37149902553751260", "1254165186821008126", "42580296599191705276", "1452739684287637542640", "49776378699192072523920", "1711962807156690517057454" ]
[ "nonn" ]
11
0
2
[ "A008485", "A322211", "A382949" ]
null
Ilya Gutkovskiy, Apr 09 2025
2025-04-10T07:24:12
oeisdata/seq/A382/A382949.seq
00817249902abadf2c79f555d06d3fbc
A382950
a(n) = [(x*y)^n] Product_{k>=1} (1 + x^k + y^k)^n.
[ "1", "0", "6", "102", "1342", "20030", "306852", "4783534", "75873934", "1220259306", "19837742836", "325375411438", "5376744428812", "89412908941096", "1494992390431000", "25114561595879252", "423649216254936110", "7172523302899053230", "121828099966104173892", "2075321708914763792740" ]
[ "nonn" ]
10
0
3
[ "A270913", "A365662", "A382950" ]
null
Ilya Gutkovskiy, Apr 09 2025
2025-04-10T06:46:01
oeisdata/seq/A382/A382950.seq
f2d9259755daf74488881d7dc2fe865c
A382951
Sequence of positive integers with no repetitions and, when put in a spiral, all lines (straight or diagonal) are pairwise coprime.
[ "1", "2", "3", "5", "4", "7", "11", "9", "13", "17", "19", "23", "8", "29", "31", "27", "25", "37", "39", "16", "41", "43", "14", "47", "33", "53", "35", "59", "61", "67", "71", "73", "49", "79", "83", "89", "97", "101", "103", "55", "107", "109", "91", "113", "85", "127", "131", "137", "139", "121", "149", "151", "157", "133", "163", "65", "167", "51", "125", "173", "143", "179", "181", "191", "161", "22", "193", "169", "197", "199", "211" ]
[ "nonn", "new" ]
39
1
2
[ "A336349", "A382951" ]
null
Bryle Morga, Apr 09 2025
2025-04-16T07:26:59
oeisdata/seq/A382/A382951.seq
95054b0e7a0b8ad78b2120fdc1f05634
A382952
Maximum number of intercalates in an extended self-orthogonal diagonal Latin square of order n.
[ "0", "0", "0", "12", "0", "0", "18", "112", "72", "53" ]
[ "nonn", "more", "hard", "new" ]
16
1
4
[ "A092237", "A307164", "A309210", "A309598", "A309599", "A360223", "A382952", "A382957" ]
null
Eduard I. Vatutin, Apr 09 2025
2025-04-23T18:14:42
oeisdata/seq/A382/A382952.seq
304a30f45ad89827ccf394a6948defa5
A382953
Numbers with at least one factorization for which the factors can be partitioned into 2 or more distinct subsets with equal sums.
[ "16", "30", "48", "54", "64", "70", "72", "84", "96", "120", "126", "128", "144", "160", "162", "180", "192", "198", "210", "216", "240", "243", "250", "252", "256", "264", "270", "280", "286", "288", "300", "308", "320", "324", "330", "336", "360", "378", "384", "390", "396", "400", "420", "432", "440", "448", "462", "468", "480", "486", "495", "504", "510", "512" ]
[ "nonn" ]
12
1
1
[ "A083207", "A255265", "A322657", "A382953" ]
null
Charles L. Hohn, Apr 09 2025
2025-04-12T12:46:37
oeisdata/seq/A382/A382953.seq
7270fb4c7e60b31b9a4786bb2a24fe57
A382954
Number of ways to partition distinct prime numbers into three disjoint sets such that the sum of each set equals n.
[ "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "2", "0", "1", "0", "1", "3", "2", "8", "1", "1", "4", "0", "14", "9", "1", "4", "7", "16", "26", "31", "17", "3", "19", "39", "54", "20", "62", "9", "41", "96", "89", "62", "66", "34", "59", "197", "241", "289", "69", "124", "184", "133", "481", "440", "148", "225", "394", "709", "808", "984", "555", "414", "799" ]
[ "nonn" ]
16
0
25
[ "A000607", "A258281", "A382871", "A382954" ]
null
Seiichi Manyama, Apr 10 2025
2025-04-10T08:34:46
oeisdata/seq/A382/A382954.seq
5ef94774a440c7c723fbabe6ae4977a4
A382955
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = [x^n * y^k] Product_{p prime} (1 + x^p + y^p).
[ "1", "0", "0", "1", "0", "1", "1", "0", "0", "1", "0", "0", "0", "0", "0", "2", "0", "1", "1", "0", "2", "0", "0", "0", "0", "0", "0", "0", "2", "0", "1", "0", "0", "1", "0", "2", "1", "0", "0", "1", "0", "1", "0", "0", "1", "1", "0", "1", "0", "0", "0", "0", "1", "0", "1", "2", "0", "1", "2", "0", "2", "0", "2", "1", "0", "2", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "2", "0", "1", "1", "0", "2", "0", "2", "0", "1", "1", "0", "2" ]
[ "nonn", "tabl" ]
14
0
16
[ "A000004", "A000586", "A284593", "A382871", "A382955", "A382956" ]
null
Seiichi Manyama, Apr 10 2025
2025-04-10T06:48:19
oeisdata/seq/A382/A382955.seq
85e0ce7dd9096b122417c73c7a55429a
A382956
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = [x^n * y^k] Product_{p prime} 1/(1 - x^p - y^p).
[ "1", "0", "0", "1", "0", "1", "1", "0", "0", "1", "1", "0", "2", "0", "1", "2", "0", "1", "1", "0", "2", "2", "0", "3", "2", "3", "0", "2", "3", "0", "3", "1", "1", "3", "0", "3", "3", "0", "5", "3", "6", "3", "5", "0", "3", "4", "0", "6", "4", "4", "4", "4", "6", "0", "4", "5", "0", "8", "4", "11", "8", "11", "4", "8", "0", "5", "6", "0", "10", "6", "10", "9", "9", "10", "6", "10", "0", "6", "7", "0", "13", "8", "19", "13", "28", "13", "19", "8", "13", "0", "7" ]
[ "nonn", "tabl" ]
12
0
13
[ "A000004", "A000607", "A322210", "A382955", "A382956" ]
null
Seiichi Manyama, Apr 10 2025
2025-04-10T06:48:29
oeisdata/seq/A382/A382956.seq
a69c1b807a1032848d34cf7dcb3aa366
A382957
a(n) is the number of distinct numbers of intercalates extended self-orthogonal diagonal Latin squares of order n.
[ "1", "0", "0", "1", "1", "0", "3", "8", "52", "45" ]
[ "nonn", "more", "hard", "new" ]
4
1
7
[ "A309210", "A309598", "A309599", "A329685", "A345760", "A382952", "A382957" ]
null
Eduard I. Vatutin, Apr 10 2025
2025-04-16T19:34:51
oeisdata/seq/A382/A382957.seq
628cc75d6df9b6d5fbb31856da4853d8
A382958
a(n) = (n!)^2 * [(x*y)^n] Product_{k>=1} 1 / (1 - (x^k + y^k)/k!).
[ "1", "2", "30", "920", "53078", "4828892", "643086588", "117718532696", "28378716172822", "8713799596723484", "3320414836230009080", "1537509304647364575716", "850310874146059999520372", "553587598414859641796343780", "419087377790397643526857611312", "365040505934072220586791778761920" ]
[ "nonn", "changed" ]
12
0
2
[ "A005651", "A322211", "A382958" ]
null
Ilya Gutkovskiy, Apr 10 2025
2025-04-25T06:34:24
oeisdata/seq/A382/A382958.seq
4901483577627f3c1de94b2fafc98567
A382959
a(n) = (n!)^2 * [(x*y)^n] Product_{k>=1} (1 + (x^k + y^k)/k!).
[ "1", "0", "0", "6", "8", "130", "342", "2590", "21240", "167730", "1874930", "46128610", "417338462", "5163377570", "542567363366", "3984766703746", "42736508056760", "681324935577810", "127138303030260258", "1011227775808000450", "14280379156264610778", "276342548314653322270", "12566141342987866203746" ]
[ "nonn", "changed" ]
11
0
4
[ "A007837", "A108796", "A365662", "A382959" ]
null
Ilya Gutkovskiy, Apr 10 2025
2025-04-24T05:59:00
oeisdata/seq/A382/A382959.seq
2c5962c50b8322320784d8f657c33f93
A382960
Numbers k such that k < A053669(k)^2 * A380539(k)^2, i.e., k < A382767(k).
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "38", "39", "40", "42", "44", "45", "46", "48", "50", "51", "52", "54", "56", "57", "58", "60", "62", "63", "64", "66", "68", "69", "70", "72", "74", "75", "76", "78", "80", "81", "82", "84" ]
[ "nonn", "easy", "fini", "full", "new" ]
22
1
2
[ "A048597", "A051250", "A053669", "A286708", "A380539", "A382659", "A382767", "A382960" ]
null
Michael De Vlieger, Apr 14 2025
2025-04-19T18:06:51
oeisdata/seq/A382/A382960.seq
470f129d06830fbfb95043b1ce2e89ad
A382961
A sequence constructed so that the probability of occurrence of integer i > 0 matches the logarithmic distribution for parameter value 1/2, 1/(log(2)*(2^i)*i).
[ "1", "1", "2", "1", "1", "3", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "4", "1", "1", "2", "1", "1", "1", "3", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "5", "1", "1", "2", "1", "1", "1", "2", "1", "1", "3", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "3", "1", "2", "1", "1", "1", "1", "2", "1", "1", "4", "1", "1", "2", "1", "1", "1", "3", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "3", "1", "1", "2", "1", "1", "1", "6", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "3", "1", "2", "1", "1", "1", "4", "1", "1", "2", "1", "1", "1", "2" ]
[ "nonn", "new" ]
14
1
3
[ "A381617", "A381898", "A381900", "A382961", "A383238" ]
null
Jwalin Bhatt, Apr 10 2025
2025-04-28T00:03:55
oeisdata/seq/A382/A382961.seq
d143bce2e3b8f1b9c3cbf48f6074a319
A382962
Number of symmetric ternary maps f : S X S X S -> S on a set S of n elements which can be represented as a superposition of binary maps * : S X S -> S.
[ "1", "5", "48", "831", "21320", "772422" ]
[ "nonn", "hard", "more", "changed" ]
18
1
2
[ "A283840", "A283841", "A382962" ]
null
Bert Dobbelaere, Apr 10 2025
2025-04-25T20:41:06
oeisdata/seq/A382/A382962.seq
5a2d99ea44bf7008828ce5b47a2aca92
A382963
Prime index gaps between consecutive full reptend primes.
[ "3", "1", "1", "1", "5", "2", "1", "7", "4", "1", "2", "3", "4", "2", "1", "2", "4", "2", "1", "4", "1", "1", "8", "3", "5", "2", "1", "1", "4", "3", "5", "4", "1", "1", "1", "1", "3", "5", "1", "2", "6", "4", "2", "6", "1", "2", "3", "9", "1", "1", "5", "2", "4", "5", "1", "2", "2", "1", "1", "5", "1", "2", "3", "2", "1", "1", "1", "2", "1", "1", "5", "2", "1", "2", "3", "1", "1", "4", "5", "1", "1", "1", "4", "2", "2", "5", "1" ]
[ "nonn", "easy" ]
18
1
1
[ "A000040", "A000720", "A001913", "A060257", "A382963" ]
null
Kyle Wyonch, Apr 10 2025
2025-04-10T17:05:22
oeisdata/seq/A382/A382963.seq
893134ec4dbe0aaa7a8de1be1e6fee3c
A382965
The number of non-unitary prime divisors of the n-th cubefree number that is not squarefree.
[ "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "2", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1" ]
[ "nonn", "easy" ]
9
1
8
[ "A002117", "A013661", "A046660", "A056170", "A067259", "A369427", "A376366", "A382965", "A382966", "A382968" ]
null
Amiram Eldar, Apr 10 2025
2025-04-11T08:46:18
oeisdata/seq/A382/A382965.seq
c78fbf7a5096e555d5ed7409bff8c788
A382966
The number of non-unitary prime divisors of the n-th biquadratefree number that is not cubefree.
[ "1", "1", "1", "1", "1", "1", "2", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "2", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "2", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1" ]
[ "nonn", "easy" ]
7
1
7
[ "A002117", "A013662", "A056170", "A375072", "A376366", "A382425", "A382965", "A382966", "A382968" ]
null
Amiram Eldar, Apr 10 2025
2025-04-11T08:46:32
oeisdata/seq/A382/A382966.seq
88f7501339cdcc547445374260fb4885
A382967
Biquadratefree numbers (A046100) that are not squarefree (A005117).
[ "4", "8", "9", "12", "18", "20", "24", "25", "27", "28", "36", "40", "44", "45", "49", "50", "52", "54", "56", "60", "63", "68", "72", "75", "76", "84", "88", "90", "92", "98", "99", "100", "104", "108", "116", "117", "120", "121", "124", "125", "126", "132", "135", "136", "140", "147", "148", "150", "152", "153", "156", "164", "168", "169", "171", "172", "175", "180", "184" ]
[ "nonn", "easy", "changed" ]
21
1
1
[ "A004709", "A005117", "A013929", "A046100", "A051903", "A059956", "A067259", "A215267", "A252849", "A375072", "A375229", "A382967" ]
null
Amiram Eldar, Apr 10 2025
2025-04-22T06:31:46
oeisdata/seq/A382/A382967.seq
5456be5784684cfde9bf001f0f738e30
A382968
The number of non-unitary prime divisors of the n-th biquadratefree number that is not squarefree.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "2", "1", "2", "1", "1", "1", "2", "1", "2", "1", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1" ]
[ "nonn", "easy" ]
7
1
11
[ "A056170", "A382425", "A382965", "A382966", "A382967", "A382968" ]
null
Amiram Eldar, Apr 10 2025
2025-04-11T08:16:10
oeisdata/seq/A382/A382968.seq
5768891038ab5972b52b5494dfd624bd
A382969
The excess of the n-th noncubefree number.
[ "2", "3", "2", "2", "4", "2", "3", "2", "2", "5", "3", "3", "3", "2", "4", "2", "3", "3", "2", "2", "6", "2", "2", "4", "2", "4", "3", "2", "3", "2", "2", "5", "3", "3", "4", "4", "2", "3", "4", "2", "2", "7", "2", "2", "3", "2", "5", "2", "2", "3", "2", "5", "4", "2", "3", "2", "2", "2", "4", "3", "3", "2", "2", "2", "6", "3", "4", "3", "2", "4", "2", "5", "2", "5", "2", "2", "3", "2", "4", "4", "2", "3", "3", "3", "8", "2", "2" ]
[ "nonn", "easy", "changed" ]
11
1
1
[ "A002117", "A046099", "A046660", "A136141", "A275699", "A376366", "A382969" ]
null
Amiram Eldar, Apr 10 2025
2025-04-14T06:18:10
oeisdata/seq/A382/A382969.seq
a1e9d19a564a6d129531c300574a1b95
A382970
Numbers k such that {k, k+2, k+6, k+8, k+90, k+92, k+96, k+98} are all prime.
[ "11", "101", "15641", "3512981", "6655541", "20769311", "26919791", "41487071", "71541641", "160471601", "189425981", "236531921", "338030591", "409952351", "423685721", "431343461", "518137091", "543062621", "588273221", "637272191", "639387311", "647851571", "705497951", "726391571", "843404201", "895161341", "958438751", "960813851", "964812461", "985123961" ]
[ "nonn", "new" ]
8
1
1
[ "A007530", "A059925", "A128467", "A382970" ]
null
David Mellinger, Apr 10 2025
2025-04-18T17:41:34
oeisdata/seq/A382/A382970.seq
a376b6fff94bdf586db28a569c99f02b
A382971
Population of elementary triangular automaton rule 146 at generation n, starting from a lone 1 cell at generation 0.
[ "1", "4", "7", "13", "7", "28", "25", "46", "13", "46", "43", "79", "49", "133", "73", "160", "55", "109", "91", "211", "73", "238", "199", "337", "133", "343", "187", "388", "211", "523", "277", "607", "205", "478", "241", "559", "259", "679", "361", "748", "379", "805", "493", "967", "523", "1042", "709", "1372", "391", "976", "709", "1501", "649", "1612", "895" ]
[ "nonn", "new" ]
7
0
2
[ "A372581", "A380012", "A380670", "A381734", "A382971", "A382972", "A383028" ]
null
Paul Cousin, Apr 10 2025
2025-04-18T21:38:45
oeisdata/seq/A382/A382971.seq
e58209bcddcf74a0e3010753bb07b4a6
A382972
Second center column of elementary triangular automaton rule 146, starting from a lone 1 cell.
[ "0", "1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "0", "0" ]
[ "nonn", "new" ]
7
0
null
[ "A374413", "A374769", "A380172", "A382971", "A382972", "A383028" ]
null
Paul Cousin, Apr 10 2025
2025-04-18T21:32:01
oeisdata/seq/A382/A382972.seq
bb6de3b88eaa9988f633f398819ac513
A382974
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = [x^n * y^k] Product_{j>=1} 1/(1 - x^j + y^j).
[ "1", "-1", "1", "0", "-2", "2", "-1", "2", "-4", "3", "1", "-3", "4", "-7", "5", "-1", "4", "-8", "10", "-12", "7", "1", "-5", "14", "-20", "18", "-19", "11", "-1", "6", "-18", "34", "-40", "34", "-30", "15", "2", "-7", "22", "-51", "78", "-77", "56", "-45", "22", "-2", "9", "-30", "75", "-127", "157", "-139", "94", "-67", "30", "2", "-11", "42", "-105", "196", "-282", "306", "-239", "146", "-97", "42" ]
[ "sign", "tabl" ]
12
0
5
[ "A000007", "A000041", "A000070", "A081362", "A304631", "A322210", "A382974", "A382979" ]
null
Seiichi Manyama, Apr 11 2025
2025-04-11T07:55:39
oeisdata/seq/A382/A382974.seq
19c42e81c7f07bc583dcacb1401ccf19
A382975
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = [x^n * y^k] Product_{j>=1} (1 + x^j - y^j).
[ "1", "-1", "1", "-1", "0", "1", "0", "-1", "-1", "2", "0", "-1", "0", "-1", "2", "1", "-1", "-1", "-1", "-1", "3", "0", "0", "0", "0", "-2", "-2", "4", "1", "0", "0", "-2", "0", "-2", "-2", "5", "0", "1", "0", "-1", "0", "-1", "-2", "-3", "6", "0", "1", "1", "0", "-1", "-1", "-2", "-3", "-3", "8", "0", "1", "0", "0", "-1", "2", "-1", "-2", "-4", "-5", "10", "0", "1", "1", "0", "1", "-2", "0", "-1", "-2", "-5", "-5", "12" ]
[ "sign", "tabl" ]
14
0
10
[ "A000007", "A000009", "A010815", "A015744", "A025147", "A078616", "A284593", "A297054", "A382975", "A382980" ]
null
Seiichi Manyama, Apr 11 2025
2025-04-11T07:55:33
oeisdata/seq/A382/A382975.seq
70cec0de05021ad1ffc80af43a5784a6
A382976
Expansion of Product_{k>=1} (1 + (2^k + 1) * x^k).
[ "1", "3", "5", "24", "44", "129", "384", "897", "2220", "5706", "15268", "35178", "89829", "212982", "526222", "1294263", "3087570", "7300896", "17726100", "41705904", "98782950", "236059794", "551697495", "1293417672", "3033232130", "7081297146", "16430673765", "38347412562", "88762751808", "204970377366", "473719894598" ]
[ "nonn" ]
22
0
2
[ "A000051", "A079555", "A266964", "A284593", "A322199", "A382976", "A382977", "A382978" ]
null
Seiichi Manyama, Apr 11 2025
2025-04-11T11:16:15
oeisdata/seq/A382/A382976.seq
6a46c35486e30dc6887a78c1ee92a8fb
A382977
Expansion of Product_{k>=1} 1/(1 - (2^k - 1) * x^k).
[ "1", "1", "4", "11", "35", "87", "271", "659", "1908", "4832", "13132", "32688", "89109", "218385", "571489", "1427388", "3652877", "8980805", "22858201", "55822728", "140065621", "342001192", "845707856", "2052802367", "5057431745", "12197383588", "29738238996", "71604414162", "173406091548", "415167136507", "1000881376700" ]
[ "nonn" ]
21
0
3
[ "A000225", "A266964", "A322199", "A382976", "A382977", "A382978" ]
null
Seiichi Manyama, Apr 11 2025
2025-04-13T16:21:32
oeisdata/seq/A382/A382977.seq
d238348afa8d26be9290ad24941fb2be
A382978
Expansion of Product_{k>=1} (1 + (2^k - 1) * x^k).
[ "1", "1", "3", "10", "22", "67", "160", "433", "986", "2774", "6386", "16214", "39201", "95868", "229644", "569707", "1324730", "3186326", "7664378", "17955006", "42497434", "100710158", "235492595", "549267552", "1288847672", "2990756088", "6958113345", "16148883002", "37286262238", "85880711282", "198840926982", "454980392570" ]
[ "nonn", "changed" ]
23
0
3
[ "A000225", "A048651", "A266964", "A322199", "A382976", "A382977", "A382978" ]
null
Seiichi Manyama, Apr 11 2025
2025-04-14T07:38:54
oeisdata/seq/A382/A382978.seq
a936808aa6ddca32d17b312b5c30079e
A382979
a(n) = [(x*y)^n] Product_{k>=1} 1/(1 - x^k + y^k).
[ "1", "-2", "4", "-20", "78", "-282", "1048", "-4014", "15456", "-59224", "227646", "-879694", "3407730", "-13219372", "51375286", "-200021556", "779870542", "-3044448644", "11898709560", "-46553635346", "182315752476", "-714619687038", "2803342734160", "-11005274516610", "43233909672938", "-169951684067602", "668474115081988" ]
[ "sign" ]
15
0
2
[ "A100221", "A322211", "A382974", "A382979" ]
null
Seiichi Manyama, Apr 11 2025
2025-04-13T13:39:43
oeisdata/seq/A382/A382979.seq
8b1491e98bbe49c23c9a8f581161e9c1
A382980
a(n) = [(x*y)^n] Product_{k>=1} (1 + x^k - y^k).
[ "1", "0", "0", "0", "0", "2", "0", "4", "2", "6", "4", "10", "6", "14", "10", "14", "10", "20", "6", "22", "2", "10", "14", "16", "-32", "14", "6", "-26", "-20", "12", "-56", "28", "-2", "-38", "96", "56", "-38", "200", "298", "82", "338", "460", "446", "666", "852", "456", "1580", "1172", "1048", "1608", "2426", "1236", "2810", "2222", "2824", "2066", "3716", "1612", "5498" ]
[ "sign", "changed" ]
17
0
6
[ "A365662", "A382975", "A382980" ]
null
Seiichi Manyama, Apr 11 2025
2025-04-14T17:32:54
oeisdata/seq/A382/A382980.seq
cfbaa8b8b1b923ca8e4d83525bb2327f
A382981
The smallest n-digit prime that turns composite at each step as its digits are successively appended, starting from the last.
[ "2", "11", "101", "1019", "10007", "100043", "1000003", "10000019", "100000007", "1000000007", "10000000019", "100000000003", "1000000000039", "10000000000037", "100000000000031", "1000000000000037", "10000000000000061", "100000000000000003", "1000000000000000003", "10000000000000000051" ]
[ "nonn", "base", "changed" ]
22
1
1
[ "A003617", "A382899", "A382981" ]
null
Jean-Marc Rebert, Apr 11 2025
2025-04-16T10:30:06
oeisdata/seq/A382/A382981.seq
fcc2e1cf336b279c3d05e4dd871b6e57
A382982
Primes of the form Sum_{i=j..k} prime(i)^prime(i).
[ "31", "826699", "303160419086407" ]
[ "nonn", "new" ]
18
1
1
[ "A051674", "A061789", "A340392", "A382982" ]
null
Zak Seidov and Robert Israel, Apr 11 2025
2025-04-17T09:51:37
oeisdata/seq/A382/A382982.seq
617384b161b19dab6ef1ad8d74f4ab52
A382983
a(n) is the number of solutions to n = x*y in positive integers x <= y where x + y is prime.
[ "1", "1", "0", "1", "0", "2", "0", "0", "0", "2", "0", "2", "0", "0", "0", "1", "0", "2", "0", "0", "0", "2", "0", "1", "0", "0", "0", "2", "0", "4", "0", "0", "0", "1", "0", "2", "0", "0", "0", "2", "0", "4", "0", "0", "0", "1", "0", "1", "0", "0", "0", "2", "0", "1", "0", "0", "0", "2", "0", "4", "0", "0", "0", "0", "0", "2", "0", "0", "0", "4", "0", "2", "0", "0", "0", "1", "0", "4", "0", "0", "0", "2", "0", "2", "0", "0", "0", "2" ]
[ "nonn", "easy", "new" ]
12
1
6
[ "A000040", "A004526", "A038548", "A382983", "A382984", "A382985" ]
null
Felix Huber, Apr 14 2025
2025-04-19T17:49:29
oeisdata/seq/A382/A382983.seq
85e78e78e47c6349b4c6118852770272
A382984
Coefficient of x^3 in expansion of (x+1) * (x+4) * ... * (x+3*n-2).
[ "0", "0", "0", "1", "22", "445", "9605", "227969", "5974388", "172323696", "5441287980", "187011672276", "6957458412520", "278765196526024", "11973706678705408", "549052544309039744", "26777325537157361024", "1384271732837081576576", "75622395021091990225152", "4353640204459556218940160" ]
[ "nonn", "new" ]
9
0
5
[ "A028340", "A286718", "A382984" ]
null
Seiichi Manyama, Apr 20 2025
2025-04-20T08:40:48
oeisdata/seq/A382/A382984.seq
e03985dbb1b5429f0eea19960f02da6e
A382985
Coefficient of x^4 in expansion of (x+1) * (x+4) * ... * (x+3*n-2).
[ "0", "0", "0", "0", "1", "35", "1005", "28700", "859369", "27458613", "941164860", "34617398640", "1364003226036", "57425577775852", "2575788307560104", "122732603903789880", "6194752323883374224", "330320189407442698000", "18560921582024101872576", "1096473082032417593216832" ]
[ "nonn", "new" ]
9
0
6
[ "A028341", "A286718", "A382985" ]
null
Seiichi Manyama, Apr 20 2025
2025-04-20T08:40:44
oeisdata/seq/A382/A382985.seq
da443dac1b26008b075d817a699335d3
A382986
a(n) is the number of iterations that n requires to reach 0 under the map k -> b(k) where b(k) = k+1 if k is even, and b(k) = k-gpf(k) if k is odd, where gpf(k) is the greatest prime dividing k.
[ "0", "1", "2", "1", "2", "1", "2", "1", "4", "3", "2", "1", "2", "1", "4", "3", "2", "1", "2", "1", "6", "5", "2", "1", "8", "7", "10", "9", "2", "1", "2", "1", "4", "3", "4", "3", "2", "1", "12", "11", "2", "1", "2", "1", "4", "3", "2", "1", "4", "3", "6", "5", "2", "1", "6", "5", "14", "13", "2", "1", "2", "1", "16", "15", "4", "3", "2", "1", "4", "3", "2", "1", "2", "1", "4", "3", "4", "3", "2", "1", "4", "3", "2", "1", "6", "5", "4", "3", "2", "1" ]
[ "nonn", "new" ]
54
0
3
[ "A006530", "A076563", "A382986" ]
null
Jakub Buczak, Apr 11 2025
2025-04-24T00:16:20
oeisdata/seq/A382/A382986.seq
05011b2b429b172aaf8e20f2229a61e0
A382987
a(n) is the total sum of the last symbol in all Catalan words of length n avoiding the pattern (>=,>=).
[ "0", "0", "1", "4", "12", "34", "94", "258", "707", "1940", "5337", "14728", "40777", "113268", "315627", "882168", "2472669", "6949344", "19579971", "55296972", "156511626", "443902074", "1261440936", "3591153874", "10240960381", "29251149324", "83675868455", "239703961016", "687596129964", "1974890635522", "5679036727894" ]
[ "nonn" ]
9
0
4
[ "A382987", "A382988", "A382989", "A382990" ]
null
Stefano Spezia, Apr 11 2025
2025-04-12T12:36:44
oeisdata/seq/A382/A382987.seq
23dce0dfaf86507c80d4571147bc41e6
A382988
a(n) is the total sum of semiperimeters over all (>=,>=)-polyominoes of length n.
[ "0", "2", "7", "21", "62", "180", "522", "1512", "4384", "12726", "36995", "107701", "313986", "916604", "2679159", "7840125", "22967784", "67352334", "197693325", "580775223", "1707553410", "5024194308", "14793209508", "43585511382", "128495325672", "379036691250", "1118687153077", "3303357347907", "9759086504006", "28844148674092" ]
[ "nonn" ]
9
0
2
[ "A382987", "A382988", "A382989", "A382990" ]
null
Stefano Spezia, Apr 11 2025
2025-04-12T12:37:15
oeisdata/seq/A382/A382988.seq
9c43785492d87ef00504899c86276c79
A382989
a(n) is the total sum of area over all (>=,>=)-polyominoes of length n.
[ "0", "1", "5", "19", "66", "218", "701", "2215", "6919", "21438", "66034", "202502", "618892", "1886433", "5737755", "17421735", "52823013", "159970938", "483979572", "1463006976", "4419285573", "13340964849", "40252007970", "121389925346", "365929470596", "1102688346763", "3321748158985", "10003556543907", "30118208180650" ]
[ "nonn" ]
11
0
3
[ "A002426", "A382987", "A382988", "A382989", "A382990" ]
null
Stefano Spezia, Apr 11 2025
2025-04-12T12:37:31
oeisdata/seq/A382/A382989.seq
b39f8139744d382a923b8907d2b88440
A382990
a(n) is the total number of interior points of over all (>=,>=)-polyominoes of length n.
[ "0", "0", "0", "2", "13", "59", "230", "830", "2858", "9547", "31227", "100599", "320417", "1011664", "3172230", "9892182", "30708696", "94975383", "292822629", "900431037", "2762584182", "8459318100", "25859561685", "78934174379", "240626872721", "732695058014", "2228730824384", "6773206968802", "20567144954853", "62406771069411" ]
[ "nonn" ]
12
0
4
[ "A002426", "A382987", "A382988", "A382989", "A382990" ]
null
Stefano Spezia, Apr 11 2025
2025-04-12T12:37:41
oeisdata/seq/A382/A382990.seq
6de41128f61d80927a654f3c3e57b545
A382991
Number of compositions of n such that any part 1 at position k can be k different colors.
[ "1", "1", "3", "10", "40", "193", "1110", "7473", "57821", "505945", "4940354", "53248874", "627848885", "8037734930", "111017325473", "1645384681765", "26044845197881", "438499277779636", "7824114643731522", "147476551001255125", "2928074880767254238", "61078483577649288463", "1335438738400978511877" ]
[ "nonn", "easy", "changed" ]
14
0
3
[ "A008275", "A011782", "A088305", "A238351", "A240736", "A382991", "A382992" ]
null
John Tyler Rascoe, Apr 11 2025
2025-04-24T08:01:52
oeisdata/seq/A382/A382991.seq
c60d974c7d5ff07ccdb2f6906e4b8049
A382992
Number of compositions of n that have at least 1 part equal to 1 and any part 1 at position k can be k different colors.
[ "0", "1", "2", "9", "38", "190", "1105", "7465", "57808", "505924", "4940320", "53248819", "627848796", "8037734786", "111017325240", "1645384681388", "26044845197271", "438499277778649", "7824114643729925", "147476551001252541", "2928074880767250057", "61078483577649281698", "1335438738400978500931" ]
[ "nonn", "easy", "changed" ]
22
0
3
[ "A000045", "A008275", "A011782", "A088305", "A238351", "A240736", "A382991", "A382992" ]
null
John Tyler Rascoe, Apr 11 2025
2025-04-24T07:59:22
oeisdata/seq/A382/A382992.seq
99ff1a2a6e6bbe285122cb8ec945770d
A382993
Square array A(n,k), n >= 1, k >= 1, read by antidiagonals downwards, where A(n,k) = -(1/n) * Sum_{d|n} phi(n/d) * (-k)^d.
[ "1", "2", "0", "3", "-1", "1", "4", "-3", "4", "0", "5", "-6", "11", "-4", "1", "6", "-10", "24", "-21", "8", "0", "7", "-15", "45", "-66", "51", "-10", "1", "8", "-21", "76", "-160", "208", "-119", "20", "0", "9", "-28", "119", "-330", "629", "-676", "315", "-34", "1", "10", "-36", "176", "-609", "1560", "-2590", "2344", "-831", "60", "0", "11", "-45", "249", "-1036", "3367", "-7750", "11165", "-8226", "2195", "-100", "1" ]
[ "sign", "tabl" ]
19
1
2
[ "A000010", "A000035", "A074763", "A075195", "A286957", "A343465", "A343466", "A343467", "A382993", "A382994", "A382998", "A383011" ]
null
Seiichi Manyama, Apr 11 2025
2025-04-12T11:21:34
oeisdata/seq/A382/A382993.seq
6706af5cb27ba991eae899ffaa26979c
A382994
Square array A(n,k), n >= 1, k >= 1, read by antidiagonals downwards, where A(n,k) = -Sum_{d|n} phi(n/d) * (-k)^d.
[ "1", "2", "0", "3", "-2", "3", "4", "-6", "12", "0", "5", "-12", "33", "-16", "5", "6", "-20", "72", "-84", "40", "0", "7", "-30", "135", "-264", "255", "-60", "7", "8", "-42", "228", "-640", "1040", "-714", "140", "0", "9", "-56", "357", "-1320", "3145", "-4056", "2205", "-272", "9", "10", "-72", "528", "-2436", "7800", "-15540", "16408", "-6648", "540", "0" ]
[ "sign", "tabl" ]
15
1
2
[ "A000010", "A185651", "A382993", "A382994", "A382995", "A382997" ]
null
Seiichi Manyama, Apr 12 2025
2025-04-12T11:21:18
oeisdata/seq/A382/A382994.seq
67348ba940f0e79def3df92a9461f4f4
A382995
Square array A(n,k), n >= 1, k >= 1, read by antidiagonals downwards, where A(n,k) = Sum_{d|n} phi(n/d) * (-k)^(d-1).
[ "1", "1", "0", "1", "-1", "3", "1", "-2", "6", "0", "1", "-3", "11", "-8", "5", "1", "-4", "18", "-28", "20", "0", "1", "-5", "27", "-66", "85", "-30", "7", "1", "-6", "38", "-128", "260", "-238", "70", "0", "1", "-7", "51", "-220", "629", "-1014", "735", "-136", "9", "1", "-8", "66", "-348", "1300", "-3108", "4102", "-2216", "270", "0", "1", "-9", "83", "-518", "2405", "-7750", "15631", "-16452", "6585", "-500", "11" ]
[ "sign", "tabl" ]
15
1
6
[ "A000010", "A193356", "A343489", "A382994", "A382995", "A382998", "A382999", "A383000" ]
null
Seiichi Manyama, Apr 12 2025
2025-04-12T09:49:37
oeisdata/seq/A382/A382995.seq
21a93fa133b937aef40a07ce2053ad53
A382997
a(n) = -Sum_{d|n} phi(n/d) * (-n)^d.
[ "1", "-2", "33", "-264", "3145", "-46500", "823585", "-16781408", "387422001", "-9999900360", "285311670721", "-8916103472496", "302875106592409", "-11112006720145604", "437893890382391745", "-18446744078004650880", "827240261886336764449", "-39346408075098246299676", "1978419655660313589124321" ]
[ "sign" ]
8
1
2
[ "A000010", "A382994", "A382997", "A383010" ]
null
Seiichi Manyama, Apr 12 2025
2025-04-12T09:37:29
oeisdata/seq/A382/A382997.seq
202ff978d7e6a4785c6d3ba1581940c9
A382998
a(n) = Sum_{d|n} phi(n/d) * (-n)^(d-1).
[ "1", "-1", "11", "-66", "629", "-7750", "117655", "-2097676", "43046889", "-999990036", "25937424611", "-743008622708", "23298085122493", "-793714765724686", "29192926025492783", "-1152921504875290680", "48661191875666868497", "-2185911559727680349982", "104127350297911241532859" ]
[ "sign" ]
12
1
3
[ "A000010", "A382993", "A382995", "A382997", "A382998", "A383003" ]
null
Seiichi Manyama, Apr 12 2025
2025-04-12T09:37:34
oeisdata/seq/A382/A382998.seq
2e00e07275062b5f7843e751b9b3fe6c
A382999
a(n) = Sum_{d|n} phi(n/d) * (-2)^(d-1).
[ "1", "-1", "6", "-8", "20", "-30", "70", "-136", "270", "-500", "1034", "-2088", "4108", "-8134", "16440", "-32912", "65552", "-130878", "262162", "-524800", "1048740", "-2096138", "4194326", "-8390976", "16777300", "-33550348", "67109418", "-134225840", "268435484", "-536855640", "1073741854", "-2147516704", "4294969404" ]
[ "sign" ]
11
1
3
[ "A000010", "A034738", "A074763", "A382995", "A382999" ]
null
Seiichi Manyama, Apr 12 2025
2025-04-12T11:21:14
oeisdata/seq/A382/A382999.seq
a6814bc4decb10f52bcfbaa572ebf98d
A383000
a(n) = Sum_{d|n} phi(n/d) * (-3)^(d-1).
[ "1", "-2", "11", "-28", "85", "-238", "735", "-2216", "6585", "-19610", "59059", "-177428", "531453", "-1593606", "4783175", "-14351152", "43046737", "-129134082", "387420507", "-1162281100", "3486785925", "-10460294174", "31381059631", "-94143360856", "282429536825", "-847288078026", "2541865841523", "-7625599078020", "22876792454989" ]
[ "sign" ]
10
1
2
[ "A000010", "A034754", "A343465", "A382995", "A383000" ]
null
Seiichi Manyama, Apr 12 2025
2025-04-12T11:21:39
oeisdata/seq/A383/A383000.seq
815d60e7c953b0a99aaa5bd021007b0e
A383001
Smallest number with shortest addition-multiplication chain of length n.
[ "1", "2", "3", "5", "7", "13", "23", "59", "211", "619", "4282", "25819", "223918" ]
[ "nonn", "nice", "hard", "more", "new" ]
8
0
2
[ "A003064", "A230697", "A383001", "A383002" ]
null
Pontus von Brömssen, Apr 12 2025
2025-04-17T08:09:55
oeisdata/seq/A383/A383001.seq
831ff131ac2c3425a555f1b93a675803
A383002
Number of integers with a shortest addition-multiplication chain of length n.
[ "1", "1", "2", "5", "16", "63", "331", "2238", "19831", "222949", "3080625" ]
[ "nonn", "hard", "more", "new" ]
6
0
3
[ "A003065", "A230697", "A383001", "A383002" ]
null
Pontus von Brömssen, Apr 12 2025
2025-04-17T08:09:23
oeisdata/seq/A383/A383002.seq
d72db7f7bae26c4e13b0e6f79d559f6b
A383003
a(n) = Sum_{d|n} (-n)^(d-1).
[ "1", "-1", "10", "-67", "626", "-7745", "117650", "-2097671", "43046803", "-999990009", "25937424602", "-743008621115", "23298085122482", "-793714765724621", "29192926025441476", "-1152921504875286543", "48661191875666868482", "-2185911559727678460653", "104127350297911241532842" ]
[ "sign", "easy" ]
12
1
3
[ "A101561", "A101562", "A101563", "A262843", "A308814", "A382998", "A383003", "A383010", "A383012" ]
null
Seiichi Manyama, Apr 12 2025
2025-04-12T09:37:38
oeisdata/seq/A383/A383003.seq
846e1f4486bfe11ea672aa61527455d7
A383004
Exponent of the highest power of 2 dividing the n-th cubefree number.
[ "0", "1", "0", "2", "0", "1", "0", "0", "1", "0", "2", "0", "1", "0", "0", "1", "0", "2", "0", "1", "0", "0", "1", "2", "0", "1", "0", "0", "1", "0", "2", "0", "1", "0", "0", "1", "0", "2", "0", "1", "0", "0", "1", "0", "2", "0", "0", "0", "1", "0", "2", "0", "1", "0", "0", "1", "0", "2", "0", "1", "0", "0", "1", "0", "2", "0", "1", "0", "1", "0", "2", "0", "1", "0", "0", "1", "0", "2", "0", "1", "0", "0", "1", "0", "2", "0", "1" ]
[ "nonn", "easy" ]
9
1
4
[ "A004709", "A007814", "A373550", "A383004", "A383005", "A383009" ]
null
Amiram Eldar, Apr 12 2025
2025-04-12T09:42:24
oeisdata/seq/A383/A383004.seq
58c08f7265d6fb28bbfe520bc41d1d22
A383005
Exponent of the highest power of 2 dividing the n-th biquadratefree number.
[ "0", "1", "0", "2", "0", "1", "0", "3", "0", "1", "0", "2", "0", "1", "0", "0", "1", "0", "2", "0", "1", "0", "3", "0", "1", "0", "2", "0", "1", "0", "0", "1", "0", "2", "0", "1", "0", "3", "0", "1", "0", "2", "0", "1", "0", "0", "1", "0", "2", "0", "1", "0", "3", "0", "1", "0", "2", "0", "1", "0", "0", "1", "0", "2", "0", "1", "0", "3", "0", "1", "0", "2", "0", "1", "0", "1", "0", "2", "0", "1", "0", "3", "0", "1", "0", "2", "0" ]
[ "nonn", "easy" ]
7
1
4
[ "A007814", "A046100", "A254990", "A373550", "A383004", "A383005" ]
null
Amiram Eldar, Apr 12 2025
2025-04-12T09:41:35
oeisdata/seq/A383/A383005.seq
e770bb2df697cfa0d96ada9d03fbd1c0