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1999-12-11 03:00:00
2025-07-14 02:38:35
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A383957
Sum of the legs of the unique primitive Pythagorean triple whose inradius is A000108(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
[ "7", "7", "17", "71", "449", "3697", "35377", "369799", "4095521", "47297537", "564278417", "6911822737", "86538816337", "1103803791601", "14305269324961", "187980077927431", "2500329797088481", "33615543666867361", "456277457385934801", "6246438372527004961", "86175353802778434481", "1197196443885744428881", "16738118900659230353761" ]
[ "nonn", "easy", "changed" ]
21
0
1
[ "A000108", "A006007", "A058919", "A336535", "A381483", "A382114", "A383251", "A383957" ]
null
Miguel-Ángel Pérez García-Ortega, May 16 2025
2025-07-13T17:24:49
oeisdata/seq/A383/A383957.seq
3a208616e2fae3bee5c71451cfa53100
A383958
Sum of the legs of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = A000108(n) and its long leg and hypotenuse are consecutive natural numbers.
[ "1", "1", "7", "49", "391", "3527", "34847", "368081", "4089799", "47278087", "564211231", "6911587591", "86537984287", "1103800819999", "14305258627199", "187980039148049", "2500329655657799", "33615543148288199", "456277455475379999", "6246438365457952199", "86175353776521952799", "1197196443787879360799", "16738118900293300099199" ]
[ "nonn", "easy", "changed" ]
18
0
3
[ "A000108", "A001246", "A131428", "A381846", "A383615", "A383616", "A383958" ]
null
Miguel-Ángel Pérez García-Ortega, May 16 2025
2025-07-13T17:24:33
oeisdata/seq/A383/A383958.seq
dc6e4f525e51157932b899e532ff2b97
A383959
The number of prime powers p^e having the property that e is a unitary divisor of the p-adic valuation of n.
[ "0", "1", "1", "2", "1", "2", "1", "2", "2", "2", "1", "3", "1", "2", "2", "2", "1", "3", "1", "3", "2", "2", "1", "3", "2", "2", "2", "3", "1", "3", "1", "2", "2", "2", "2", "4", "1", "2", "2", "3", "1", "3", "1", "3", "3", "2", "1", "3", "2", "3", "2", "3", "1", "3", "2", "3", "2", "2", "1", "4", "1", "2", "3", "4", "2", "3", "1", "3", "2", "3", "1", "4", "1", "2", "3", "3", "2", "3", "1", "3", "2", "2", "1", "4", "2", "2", "2" ]
[ "nonn", "easy" ]
9
1
4
[ "A001221", "A034444", "A077761", "A085548", "A238949", "A278908", "A361255", "A383863", "A383959", "A383960" ]
null
Amiram Eldar, May 16 2025
2025-05-17T08:15:10
oeisdata/seq/A383/A383959.seq
93d2428794aadd5c0ac032b4957c041c
A383960
The number of prime powers p^e having the property that e is an infinitary divisor of the p-adic valuation of n.
[ "0", "1", "1", "2", "1", "2", "1", "2", "2", "2", "1", "3", "1", "2", "2", "2", "1", "3", "1", "3", "2", "2", "1", "3", "2", "2", "2", "3", "1", "3", "1", "2", "2", "2", "2", "4", "1", "2", "2", "3", "1", "3", "1", "3", "3", "2", "1", "3", "2", "3", "2", "3", "1", "3", "2", "3", "2", "2", "1", "4", "1", "2", "3", "4", "2", "3", "1", "3", "2", "3", "1", "4", "1", "2", "3", "3", "2", "3", "1", "3", "2", "2", "1", "4", "2", "2", "2" ]
[ "nonn", "easy" ]
7
1
4
[ "A037445", "A085548", "A238949", "A383760", "A383865", "A383959", "A383960" ]
null
Amiram Eldar, May 16 2025
2025-05-17T08:14:54
oeisdata/seq/A383/A383960.seq
23d2447a3cc3513f8dd3ba6720956b95
A383961
Square array read by upward antidiagonals: T(n,k) is the n-th number whose largest odd divisor is its k-th divisor, n >= 1, k >= 1.
[ "1", "2", "3", "4", "5", "6", "8", "7", "9", "15", "16", "11", "10", "20", "18", "32", "13", "12", "21", "50", "36", "64", "17", "14", "27", "81", "45", "30", "128", "19", "22", "28", "88", "63", "42", "105", "256", "23", "24", "33", "98", "75", "54", "135", "60", "512", "29", "25", "35", "104", "99", "66", "165", "84", "120", "1024", "31", "26", "39", "136", "117", "70", "189", "108", "140", "90" ]
[ "nonn", "nice", "tabl" ]
34
1
2
[ "A000005", "A000079", "A000265", "A001227", "A001248", "A001749", "A027750", "A030078", "A038547", "A046388", "A065091", "A070875", "A091629", "A100484", "A174090", "A182469", "A290110", "A383401", "A383402", "A383961" ]
null
Omar E. Pol, May 16 2025
2025-05-22T23:23:19
oeisdata/seq/A383/A383961.seq
078e8cc4a44f515f2c8db8f995acd714
A383962
Irregular triangle read by rows: T(n,k) is the index of the k-th odd divisor in the list of divisors of n, with n >= 1, k >= 1.
[ "1", "1", "1", "2", "1", "1", "2", "1", "3", "1", "2", "1", "1", "2", "3", "1", "3", "1", "2", "1", "3", "1", "2", "1", "3", "1", "2", "3", "4", "1", "1", "2", "1", "3", "5", "1", "2", "1", "4", "1", "2", "3", "4", "1", "3", "1", "2", "1", "3", "1", "2", "3", "1", "3", "1", "2", "3", "4", "1", "4", "1", "2", "1", "3", "4", "7", "1", "2", "1", "1", "2", "3", "4", "1", "3", "1", "2", "3", "4", "1", "3", "6", "1", "2", "1", "3", "1", "2", "3", "4", "1", "4", "1", "2", "1", "3", "5", "7", "1", "2", "1", "4", "1", "2", "3", "4", "5", "6" ]
[ "nonn", "tabf" ]
12
1
4
[ "A000005", "A000012", "A000027", "A000079", "A001227", "A027750", "A065091", "A174090", "A182469", "A383401", "A383962" ]
null
Omar E. Pol, May 26 2025
2025-05-30T16:05:52
oeisdata/seq/A383/A383962.seq
c2b91b983c1bfcc5d9b0fd3a5ff660a2
A383963
Irregular triangle read by rows: T(n,k) is the sum of the k-th pair of conjugate divisors of n. If n is a square then the central term in the row n is equal to 2*sqrt(n), with n >= 1, 1 <= k <= A000005(n).
[ "2", "3", "3", "4", "4", "5", "4", "5", "6", "6", "7", "5", "5", "7", "8", "8", "9", "6", "6", "9", "10", "6", "10", "11", "7", "7", "11", "12", "12", "13", "8", "7", "7", "8", "13", "14", "14", "15", "9", "9", "15", "16", "8", "8", "16", "17", "10", "8", "10", "17", "18", "18", "19", "11", "9", "9", "11", "19", "20", "20", "21", "12", "9", "9", "12", "21", "22", "10", "10", "22", "23", "13", "13", "23", "24", "24", "25", "14", "11", "10", "10", "11", "14", "25" ]
[ "nonn", "tabf" ]
39
1
1
[ "A000005", "A000027", "A000203", "A027750", "A056538", "A074400", "A237270", "A272025", "A383963" ]
null
Omar E. Pol, Jun 17 2025
2025-06-25T00:35:00
oeisdata/seq/A383/A383963.seq
1b27fa255ee017b370b17c4311a00d72
A383964
Integers k such that there exists an integer 0<m<k such that (1/sigma(m)^2 + 1/sigma(k)^2)*(m+k)^2 = 1.
[ "168", "1320", "3792", "4968", "7176", "8184", "14364", "15240", "20076", "29904", "30672", "41952", "48312", "48768", "54264", "56856", "57960", "60144", "64296", "72996", "73344", "83328", "90552", "91512", "99828", "106020", "110952", "113280", "114156", "119016", "128592", "149292", "150024", "151272", "157608", "168588", "175584", "183240" ]
[ "nonn" ]
30
1
1
[ "A063990", "A259180", "A383239", "A383483", "A383484", "A383964" ]
null
S. I. Dimitrov, May 16 2025
2025-06-24T16:17:39
oeisdata/seq/A383/A383964.seq
586812a06035397bf505958bcf39652d
A383965
Self-convolution square-root of A004381, where A004381(n) = binomial(8*n,n).
[ "1", "4", "52", "804", "13412", "233548", "4180932", "76307228", "1412731844", "26443784224", "499310856828", "9494966722696", "181620437132820", "3491268491768400", "67396227598309788", "1305787014634864584", "25380012805871145604", "494684878753394992992", "9665968233663380580256", "189289570996914582016788" ]
[ "nonn" ]
46
0
2
[ "A004381", "A208977", "A383965", "A384695" ]
null
Vaclav Kotesovec, Jun 06 2025
2025-06-07T08:13:01
oeisdata/seq/A383/A383965.seq
14df8e7c0df863c71e31fa3e2be2cc39
A383966
Numbers k such that floor(2^k / 5) is a prime.
[ "4", "11", "15", "23", "35", "71", "95", "183", "475", "579", "631", "759", "1519", "1771", "3031", "6035", "6951", "11423", "37451", "51935", "68051" ]
[ "nonn", "more" ]
18
1
1
null
null
Vincenzo Librandi, Jun 07 2025
2025-06-08T15:19:06
oeisdata/seq/A383/A383966.seq
4696c77210c5626ef219f3c260c639ea
A383967
Inventory sequence recording number of terms with 1,2,3,... decimal digits. Count until occurrence of a term = 0, whereupon reset the count; continue.
[ "0", "1", "0", "3", "0", "5", "0", "7", "0", "9", "0", "11", "1", "0", "13", "2", "0", "15", "3", "0", "17", "4", "0", "19", "5", "0", "21", "6", "0", "23", "7", "0", "25", "8", "0", "27", "9", "0", "29", "10", "0", "30", "12", "0", "31", "14", "0", "32", "16", "0", "33", "18", "0", "34", "20", "0", "35", "22", "0", "36", "24", "0", "37", "26", "0", "38", "28", "0", "39", "30", "0", "40", "32", "0", "41", "34" ]
[ "nonn", "easy" ]
21
1
4
[ "A342585", "A345730", "A347738", "A383967" ]
null
David James Sycamore, May 16 2025
2025-06-07T05:53:22
oeisdata/seq/A383/A383967.seq
9f210a0eb0907fca3eb5d625772e2d20
A383968
Number of distinct subsets S of [1..n] such that for all 1 <= k <= n, there exists two elements x,y in S (not necessarily distinct) such that x+y = 2k.
[ "1", "1", "2", "3", "5", "9", "17", "30", "58", "107", "205", "392", "768", "1466", "2883", "5597", "11038", "21572", "42675", "83711", "166371", "327893", "651199", "1288480", "2564032", "5082878", "10127472", "20115845", "40104636", "79781149", "159174500", "316962113", "632716744", "1261189166", "2518287361", "5023170116", "10034132101", "20025033970" ]
[ "nonn" ]
23
1
3
null
null
SiYang Hu, May 16 2025
2025-05-29T00:12:01
oeisdata/seq/A383/A383968.seq
7abf2c1aa3f0e0f673e021681132069d
A383969
a(n) is the smallest even number m such that the set {m+1, m+3, m+5, ..., m+(2*n-1)} contains no prime numbers.
[ "0", "24", "90", "114", "114", "114", "524", "524", "888", "1130", "1328", "1328", "1328", "1328", "1328", "1328", "9552", "15684", "15684", "15684", "15684", "19610", "19610", "19610", "19610", "31398", "31398", "31398", "31398", "31398", "31398", "31398", "31398", "31398", "31398", "155922", "155922", "155922", "155922", "155922", "155922", "155922" ]
[ "nonn" ]
17
1
2
[ "A000040", "A002386", "A002808", "A008950", "A018252", "A383969" ]
null
David James Sycamore, May 16 2025
2025-06-05T23:45:05
oeisdata/seq/A383/A383969.seq
89c31026110956a0155e340bcf41a140
A383970
Inventory sequence: record the number of prior terms such that if 2 then 4, then 6,... are added the result is a prime. Reset the count at each term = 0.
[ "0", "1", "1", "2", "0", "4", "2", "2", "0", "5", "2", "3", "2", "3", "3", "4", "5", "4", "3", "2", "2", "6", "6", "2", "2", "4", "4", "6", "6", "4", "4", "2", "2", "4", "2", "2", "6", "6", "2", "2", "4", "4", "6", "6", "2", "2", "4", "4", "4", "2", "2", "4", "2", "0", "12", "6", "4", "6", "6", "4", "6", "6", "4", "4", "2", "2", "6", "6", "2", "2", "4", "4", "6", "6", "4", "4", "2", "2", "4", "2", "2", "6", "6", "2", "2", "4", "4" ]
[ "nonn" ]
19
1
4
[ "A342585", "A383969", "A383970" ]
null
David James Sycamore, May 16 2025
2025-06-09T00:23:25
oeisdata/seq/A383/A383970.seq
55e1168b39266c65f543e018836757d8
A383971
Triprimes with sum of digits 3.
[ "12", "30", "102", "1002", "2001", "10002", "10011", "11001", "20001", "100101", "101001", "110001", "200001", "1000002", "10001001", "10010001", "11000001", "20000001", "100000101", "1000000011", "1000001001", "1000010001", "1000100001", "1001000001", "1010000001", "10000000002", "10000000011", "10000010001", "11000000001", "100000000101", "100000001001" ]
[ "nonn", "base" ]
27
1
1
[ "A001222", "A007953", "A014612", "A050689", "A052217", "A076850", "A083207", "A383971" ]
null
Robert Israel, May 16 2025
2025-06-01T10:06:43
oeisdata/seq/A383/A383971.seq
3d24c5edbe2b7657a221688e6cb2114f
A383972
Smallest number m such that (m*(m + 1)/2)^2 is divisible by n.
[ "1", "3", "2", "3", "4", "3", "6", "7", "2", "4", "10", "3", "12", "7", "5", "7", "16", "3", "18", "4", "6", "11", "22", "8", "4", "12", "8", "7", "28", "15", "30", "15", "11", "16", "14", "3", "36", "19", "12", "15", "40", "20", "42", "11", "5", "23", "46", "8", "6", "4", "17", "12", "52", "8", "10", "7", "18", "28", "58", "15", "60", "31", "6", "15", "25", "11", "66", "16", "23", "20", "70", "8", "72", "36", "5", "19", "21", "12", "78" ]
[ "nonn" ]
27
1
2
[ "A000537", "A002145", "A007520", "A011772", "A383075", "A383972" ]
null
Ctibor O. Zizka, May 16 2025
2025-05-26T21:57:57
oeisdata/seq/A383/A383972.seq
6333adb6a5525c37ea4211f694e4bde1
A383973
Irregular triangle: T(n,k) gives the number of connected subsets of k edges of the n-dimensional cross-polytope up to isometries of the polytope, with 0 <= k <= A046092(n-1).
[ "1", "1", "1", "1", "1", "1", "1", "1", "2", "5", "11", "21", "28", "24", "18", "9", "4", "1", "1", "1", "1", "2", "7", "22", "82", "292", "876", "2023", "3699", "5587", "7099", "7712", "7129", "5668", "3843", "2234", "1099", "475", "169", "57", "16", "5", "1", "1", "1", "1", "2", "7", "25", "114", "584", "3055" ]
[ "nonn", "tabf" ]
21
1
9
[ "A046092", "A333333", "A369605", "A383973" ]
null
Peter Kagey, May 16 2025
2025-05-17T00:39:33
oeisdata/seq/A383/A383973.seq
2509bdac68ea1217aff8af82a975569c
A383974
Number of connected subsets of n edges of the icosahedron up to the 120 rotations and reflections of the icosahedron.
[ "1", "1", "2", "8", "27", "126", "557", "2503", "10270", "37542", "114926", "283958", "552542", "866843", "1129291", "1250835", "1195298", "993613", "720889", "456329", "251444", "119989", "49269", "17238", "5113", "1257", "262", "46", "8", "1", "1" ]
[ "nonn", "fini", "full" ]
16
0
3
[ "A333333", "A383490", "A383973", "A383974", "A383975" ]
null
Peter Kagey, May 16 2025
2025-05-26T00:25:58
oeisdata/seq/A383/A383974.seq
9fdbf2c86d763628c0f4fbf65600fe1d
A383975
Irregular triangle: T(n,k) gives the number of connected subsets of k edges of the n-simplex up to isometries of the n-simplex, with 0 <= k <= A000217(n).
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "3", "2", "1", "1", "1", "1", "1", "3", "5", "6", "6", "4", "2", "1", "1", "1", "1", "1", "3", "5", "12", "19", "23", "24", "21", "15", "9", "5", "2", "1", "1", "1", "1", "1", "3", "5", "12", "30", "56", "91", "128", "147", "147", "131", "97", "65", "41", "21", "10", "5", "2", "1", "1", "1", "1", "1", "3", "5", "12", "30", "79", "180", "364", "633", "961", "1300", "1551", "1644", "1556", "1311", "980", "663", "402", "221", "115", "56", "24", "11", "5", "2", "1", "1" ]
[ "nonn", "tabf" ]
38
0
11
[ "A000217", "A002905", "A292300", "A333333", "A383490", "A383973", "A383974", "A383975" ]
null
Peter Kagey, May 16 2025
2025-05-28T10:53:31
oeisdata/seq/A383/A383975.seq
d25f6fc79c3601dc2d4a0fb498c604f8
A383976
In the binary expansion of n, expand bits 1 -> 11 and 0 -> 10.
[ "2", "3", "14", "15", "58", "59", "62", "63", "234", "235", "238", "239", "250", "251", "254", "255", "938", "939", "942", "943", "954", "955", "958", "959", "1002", "1003", "1006", "1007", "1018", "1019", "1022", "1023", "3754", "3755", "3758", "3759", "3770", "3771", "3774", "3775", "3818", "3819", "3822", "3823", "3834", "3835", "3838", "3839", "4010", "4011", "4014" ]
[ "nonn", "base", "easy" ]
30
0
1
[ "A000523", "A374625", "A383976" ]
null
Darío Clavijo, May 16 2025
2025-05-21T23:36:39
oeisdata/seq/A383/A383976.seq
8ed8231961097fd2410597f2430f380e
A383977
Sequence of successive merge positions when Fibonacci-sorting an infinite list.
[ "1", "2", "4", "3", "6", "7", "5", "9", "10", "12", "11", "8", "14", "15", "17", "16", "19", "20", "18", "13", "22", "23", "25", "24", "27", "28", "26", "30", "31", "33", "32", "29", "21", "35", "36", "38", "37", "40", "41", "39", "43", "44", "46", "45", "42", "48", "49", "51", "50", "53", "54", "52", "47", "34", "56", "57", "59", "58", "61", "62", "60", "64", "65", "67", "66", "63", "69", "70", "72", "71", "74", "75" ]
[ "easy", "nonn" ]
25
1
2
[ "A000045", "A383977" ]
null
Lucilla Blessing, May 16 2025
2025-05-17T22:42:35
oeisdata/seq/A383/A383977.seq
981b9c3b90fd31b30bcf0846fcbd7d10
A383978
Primes with at least two identical trailing digits.
[ "11", "199", "211", "233", "277", "311", "433", "499", "577", "599", "677", "733", "811", "877", "911", "977", "1033", "1277", "1399", "1433", "1499", "1511", "1699", "1733", "1777", "1811", "1877", "1933", "1999", "2011", "2099", "2111", "2311", "2333", "2377", "2399", "2411", "2477", "2633", "2677", "2699", "2711", "2777", "2833", "2999", "3011", "3299" ]
[ "nonn", "base" ]
20
1
1
[ "A050758", "A061022", "A131306", "A383978", "A383979", "A384013", "A384015" ]
null
Stefano Spezia, May 16 2025
2025-05-20T19:12:44
oeisdata/seq/A383/A383978.seq
f5e2eb1a9e43d2e9801403329e6bdffa
A383979
a(n) is the number of n-digit terms in A383978.
[ "0", "1", "15", "106", "821", "6909", "58683", "509654", "4508611", "40421003", "366300162", "3348975103", "30845805300", "285887726304", "2663962455661" ]
[ "nonn", "base", "more", "changed" ]
38
1
3
[ "A383978", "A383979", "A384014", "A384016" ]
null
Stefano Spezia, May 16 2025
2025-07-13T23:51:46
oeisdata/seq/A383/A383979.seq
0c653d53238d2b634d992eb4bc26ed34
A383980
Length of shortest path (in Chebyshev distance) that touches all cells in an n X n grid.
[ "0", "0", "0", "3", "6", "10", "14", "20", "25", "31", "39" ]
[ "nonn", "more" ]
43
0
4
null
null
Fülöp Tamás, May 16 2025
2025-05-18T07:57:44
oeisdata/seq/A383/A383980.seq
cb59e01a7985793e51f1fa8cedd567b7
A383981
Number of connected subsets of n edges of the rhombic dodecahedron up to the 48 rotations and reflections of the rhombic dodecahedron.
[ "1", "1", "3", "5", "16", "39", "127", "357", "1067", "2861", "7071", "14827", "25638", "33730", "33189", "24838", "14954", "7188", "2905", "912", "254", "49", "11", "1", "1" ]
[ "nonn", "fini", "full" ]
15
0
3
[ "A019988", "A333333", "A383490", "A383973", "A383974", "A383981", "A383982", "A383983", "A383984" ]
null
Peter Kagey, May 16 2025
2025-05-17T00:39:46
oeisdata/seq/A383/A383981.seq
4d8bd54af9af91fc6ca4c8746a9f5483
A383982
Number of connected subsets of n edges of the cuboctahedron up to the 48 rotations and reflections of the cuboctahedron.
[ "1", "1", "3", "7", "24", "74", "269", "876", "2788", "7639", "17828", "32326", "44375", "46456", "39213", "26865", "15470", "7278", "2917", "913", "254", "49", "11", "1", "1" ]
[ "nonn", "fini", "full" ]
11
0
3
[ "A019988", "A333333", "A383490", "A383973", "A383974", "A383981", "A383982", "A383983", "A383984" ]
null
Peter Kagey, May 16 2025
2025-05-17T00:39:51
oeisdata/seq/A383/A383982.seq
0bbc746bebbe70dad8ee2b61d65d2a6c
A383983
Number of connected subsets of n edges of the rhombic triacontahedron up to the 120 rotations and reflections of the rhombic triacontahedron.
[ "1", "1", "3", "7", "24", "84", "334", "1330", "5495", "22776", "94920", "394706" ]
[ "nonn", "fini", "more" ]
10
0
3
[ "A019988", "A333333", "A383490", "A383973", "A383974", "A383981", "A383982", "A383983", "A383984" ]
null
Peter Kagey, May 16 2025
2025-05-17T00:40:01
oeisdata/seq/A383/A383983.seq
439bc15c0022fa97d9a9defdde924625
A383984
Number of connected subsets of n edges of the icosidodecahedron up to the 120 rotations and reflections of the icosidodecahedron.
[ "1", "1", "3", "7", "24", "81", "323", "1265", "5202", "21335", "88412", "364897" ]
[ "nonn", "fini", "more" ]
9
0
3
[ "A019988", "A333333", "A383490", "A383973", "A383974", "A383981", "A383982", "A383983", "A383984" ]
null
Peter Kagey, May 16 2025
2025-05-17T00:40:08
oeisdata/seq/A383/A383984.seq
0e8e84671ae912c105716fcf02a77582
A383985
Series expansion of the exponential generating function LambertW(1-exp(x)), see A000169.
[ "0", "1", "-1", "4", "-23", "181", "-1812", "22037", "-315569", "5201602", "-97009833", "2019669961", "-46432870222", "1168383075471", "-31939474693297", "942565598033196", "-29866348653695203", "1011335905644178273", "-36446897413531401020", "1392821757824071815641", "-56259101478392975833333" ]
[ "sign", "easy" ]
17
0
4
[ "A000169", "A002050", "A006531", "A084099", "A101851", "A114285", "A177885", "A225883", "A383985", "A383986", "A383987", "A383988", "A383989" ]
null
Michael De Vlieger, May 16 2025
2025-05-24T00:21:11
oeisdata/seq/A383/A383985.seq
c83fc8ba4a60b78d6beec762be9d279a
A383986
Expansion of the exponential generating function sqrt(4*exp(x) - exp(2*x) - 2) - 1.
[ "0", "1", "-1", "1", "-13", "61", "-601", "5881", "-73333", "1021861", "-16334401", "290146561", "-5707536253", "122821558861", "-2873553719401", "72586328036041", "-1969306486088773", "57106504958139061", "-1762735601974347601", "57705363524117482321", "-1996916624448159410893" ]
[ "sign", "easy" ]
10
0
5
[ "A002050", "A006531", "A084099", "A101851", "A114285", "A182037", "A225883", "A383985", "A383986", "A383987", "A383988", "A383989" ]
null
Michael De Vlieger, May 16 2025
2025-05-21T01:26:30
oeisdata/seq/A383/A383986.seq
375377256b26e7aec1e3b27ee7a76491
A383987
Series expansion of the exponential generating function -tridend(-(1-exp(x))) where tridend(x) = (1 - 3*x - sqrt(1+6*x+x^2)) / (4*x) (A001003).
[ "0", "1", "-5", "49", "-725", "14401", "-360005", "10863889", "-384415925", "15612336481", "-715930020005", "36592369889329", "-2062911091119125", "127170577711282561", "-8510569547826528005", "614491222512504748369", "-47615614242877583230325", "3941408640018910366196641" ]
[ "sign", "easy" ]
23
0
3
[ "A001003", "A002050", "A006531", "A084099", "A101851", "A114285", "A225883", "A383985", "A383986", "A383987", "A383988", "A383989", "A383991" ]
null
Michael De Vlieger, May 16 2025
2025-05-24T00:20:56
oeisdata/seq/A383/A383987.seq
0c8336262f0f435db80b65cfa972a70a
A383988
Series expansion of the exponential generating function -postLie(1-exp(x)) where postLie(x) = -log((1 + sqrt(1-4*x)) / 2) (given by A006963).
[ "0", "1", "-2", "12", "-110", "1380", "-22022", "426972", "-9747950", "256176660", "-7617417302", "252851339532", "-9268406209790", "371843710214340", "-16206868062692582", "762569209601624892", "-38525315595630383630", "2079964082064837282420", "-119513562475103977951862" ]
[ "sign", "easy" ]
31
0
3
[ "A002050", "A006531", "A006963", "A084099", "A097388", "A101851", "A114285", "A225883", "A383985", "A383986", "A383987", "A383988", "A383989" ]
null
Michael De Vlieger, May 16 2025
2025-05-28T09:19:43
oeisdata/seq/A383/A383988.seq
1e4bd94fe28989c53f28a3c8b0a42482
A383989
Series expansion of the exponential generating function ff6^!(exp(x)-1) where ff6^!(x) = x * (1-3*x-x^2+x^3) / (1+3*x+x^2-x^3).
[ "0", "1", "-11", "61", "-467", "4381", "-49091", "643021", "-9615827", "161844541", "-3026079971", "62243374381", "-1396619164787", "33949401567901", "-888725861445251", "24926889744928141", "-745755560487363347", "23705772035082494461", "-797875590555470224931", "28346366547928396344301" ]
[ "sign", "easy" ]
17
0
3
[ "A002050", "A006531", "A084099", "A101851", "A114285", "A225883", "A383985", "A383986", "A383987", "A383988", "A383989", "A383995" ]
null
Michael De Vlieger, May 16 2025
2025-05-27T10:32:10
oeisdata/seq/A383/A383989.seq
a1e8be77114c5600ba7ef8577fd5ec1f
A383990
Series expansion of the exponential generating function exp(-dend(-x))-1 where dend(x) = (1 - sqrt(1+4*x)) / (2*x) + 1 (given by A000108).
[ "0", "1", "-3", "19", "-191", "2661", "-47579", "1040047", "-26888511", "802727209", "-27178685459", "1029077910411", "-43086906080063", "1976633329627789", "-98597207392040811", "5313105048925173991", "-307587436319162110079", "19038773384213189214417", "-1254686724727364725716131" ]
[ "sign" ]
24
0
3
[ "A000108", "A003725", "A006531", "A097388", "A111884", "A112242", "A177885", "A318215", "A383990", "A383991", "A383992", "A383993", "A383994", "A383995" ]
null
Michael De Vlieger, May 16 2025
2025-05-28T09:19:48
oeisdata/seq/A383/A383990.seq
2169985a793d1a7b6f80ec7db6ae4151
A383991
Series expansion of the exponential generating function exp(-tridend(-x)) - 1 where tridend(x) = (1 - 3*x - sqrt(1-6*x+x^2)) / (4*x) (A001003).
[ "0", "1", "-5", "49", "-743", "15421", "-407909", "13135165", "-498874991", "21838772377", "-1082819193029", "59983280191561", "-3671752681190615", "246130081055714389", "-17932045676505509093", "1410893903131294766101", "-119227840965746009631839", "10769985399394862863318705" ]
[ "sign", "easy" ]
25
0
3
[ "A003725", "A097388", "A111884", "A112242", "A177885", "A318215", "A383987", "A383990", "A383991", "A383992", "A383993", "A383994", "A383995" ]
null
Michael De Vlieger, May 16 2025
2025-05-28T09:19:19
oeisdata/seq/A383/A383991.seq
d8aef4329b298c4e4b63a8c84914dc8a
A383992
Series expansion of the exponential generating function exp(arbustive(x)) - 1 where arbustive(x) = (log(1+x) - x^2) / (1+x).
[ "0", "1", "-4", "3", "40", "-330", "1626", "-3150", "-54592", "1060920", "-13022280", "127171440", "-889086648", "-283184616", "179750627616", "-4895777544840", "99124001788800", "-1721513264431680", "25736021675994816", "-292896125040673728", "639149345262276480", "106178474282318726400" ]
[ "sign", "easy" ]
9
0
3
[ "A003725", "A097388", "A111884", "A112242", "A114285", "A177885", "A318215", "A383990", "A383991", "A383992", "A383993", "A383994", "A383995" ]
null
Michael De Vlieger, May 16 2025
2025-05-21T01:25:57
oeisdata/seq/A383/A383992.seq
a1e6c94c3653936856e994cfba214117
A383993
Series expansion of the exponential generating function exp(tridup^!(x)) - 1 where tridup^!(x) = x / ((1+x) * (1+2*x)).
[ "0", "1", "-5", "25", "-119", "301", "5611", "-171275", "3574705", "-68597639", "1282415131", "-23479249199", "409082338105", "-6146707844315", "46462772999371", "2072826643602541", "-160983324879816479", "8004468391727017585", "-352443295329194182085", "14817357881274444545161" ]
[ "sign", "easy" ]
12
0
3
[ "A002050", "A003725", "A097388", "A111884", "A112242", "A177885", "A318215", "A383990", "A383991", "A383992", "A383993", "A383994", "A383995" ]
null
Michael De Vlieger, May 16 2025
2025-05-28T16:38:18
oeisdata/seq/A383/A383993.seq
c2e0773eae3350ece78e0a42c690f155
A383994
Series expansion of the exponential generating function exp(wnp^!(x)) - 1 where wnp^!(x) = log(1+x) - x^2/(1+x).
[ "0", "1", "-2", "0", "12", "-60", "240", "-840", "1680", "15120", "-332640", "4656960", "-59209920", "735134400", "-9098369280", "112345833600", "-1365274310400", "15746578848000", "-155630893017600", "762963647846400", "22567767443020800", "-1126188650069683200", "35900904478389350400" ]
[ "sign" ]
15
0
3
[ "A003725", "A084099", "A097388", "A111884", "A112242", "A177885", "A318215", "A383990", "A383991", "A383992", "A383993", "A383994", "A383995" ]
null
Michael De Vlieger, May 16 2025
2025-05-28T16:38:00
oeisdata/seq/A383/A383994.seq
d235f9f482836fd0abdef94c92ce44f5
A383995
Series expansion of the exponential generating function exp(ff6^!(x)) - 1 where ff6^!(x) = x * (1-3*x-x^2+x^3) / (1+3*x+x^2-x^3).
[ "0", "1", "-11", "61", "-215", "-1559", "62941", "-1371131", "26310481", "-474554735", "7824076741", "-98881279859", "-176260664711", "87457412423161", "-5077434546358355", "234510433823788501", "-10016559114085864799", "413333665704129673249", "-16704968283664639137899", "660340818239784197391325" ]
[ "sign" ]
14
0
3
[ "A003725", "A097388", "A111884", "A112242", "A177885", "A318215", "A383989", "A383990", "A383991", "A383992", "A383993", "A383994", "A383995" ]
null
Michael De Vlieger, May 16 2025
2025-05-28T16:38:06
oeisdata/seq/A383/A383995.seq
268a95b397b6cb3efddfae44326c8b6a
A383996
a(n) = Product_{k=0..n-1} (n-4*k).
[ "1", "1", "-4", "15", "0", "-1155", "20160", "-208845", "0", "68139225", "-2075673600", "34976316375", "0", "-25949801752875", "1126343522304000", "-26264240610733125", "0", "34770736214117528625", "-1958486116582195200000", "58318039100493206409375", "0", "-120842042784862988395681875", "8366746697372733839769600000" ]
[ "sign", "easy" ]
16
0
3
[ "A303487", "A383996", "A384216" ]
null
Seiichi Manyama, May 22 2025
2025-05-23T02:00:42
oeisdata/seq/A383/A383996.seq
b968ecd05b6ba4e674f9f06bea55f293
A383997
a(n) = Product_{k=0..n-1} (n-5*k).
[ "1", "1", "-6", "42", "-264", "0", "57456", "-1808352", "40715136", "-643458816", "0", "583285038336", "-32763345398784", "1237080874917888", "-31193431756591104", "0", "64105508174249558016", "-5177532237241354518528", "274167069135623993032704", "-9487174826303791319678976", "0" ]
[ "sign", "easy" ]
14
0
3
[ "A303488", "A383997", "A384216" ]
null
Seiichi Manyama, May 22 2025
2025-05-23T02:00:45
oeisdata/seq/A383/A383997.seq
e34ac18ef6fd7e09232cbb3c4b2537a5
A383999
Sequence obtained by replacing 3-term subwords of A003849 by 0,1,2,3 as described in Comments.
[ "1", "2", "0", "1", "3", "1", "2", "0", "1", "2", "0", "1", "3", "1", "2", "0", "1", "3", "1", "2", "0", "1", "2", "0", "1", "3", "1", "2", "0", "1", "2", "0", "1", "3", "1", "2", "0", "1", "3", "1", "2", "0", "1", "2", "0", "1", "3", "1", "2", "0", "1", "3", "1", "2", "0", "1", "2", "0", "1", "3", "1", "2", "0", "1", "2", "0", "1", "3", "1", "2", "0", "1", "3", "1", "2", "0", "1", "2", "0", "1", "3", "1", "2", "0", "1", "2" ]
[ "nonn" ]
6
1
2
[ "A003622", "A003623", "A003849", "A035336", "A035513", "A101864", "A381848", "A383999" ]
null
Clark Kimberling, May 23 2025
2025-05-29T00:34:26
oeisdata/seq/A383/A383999.seq
27c4d57cfbfe02094452971e5ea68657
A384000
Smallest number k with n distinct prime factors such that A010846(k) = A024718(n) (a tight lower bound), or -1 if such k does not exist.
[ "1", "2", "6", "1001", "268801", "3433936673", "2603508937756211" ]
[ "nonn", "hard", "more" ]
13
0
2
[ "A001221", "A001700", "A005117", "A007947", "A010846", "A024718", "A138109", "A162306", "A383177", "A383178", "A383179", "A384000" ]
null
Michael De Vlieger, May 19 2025
2025-06-11T01:07:55
oeisdata/seq/A384/A384000.seq
7622c9409d82132fc209c34546cddb4d
A384003
Irregular triangle T(n,k), n >= 0, k = 0..2^(n-1)-1, where a(n) = Product_{j=0..n-1} prime(j+1)^((n-j)*d_j), where d_j is the bit with digit weight 2^j in the binary expansion of 2^n+k.
[ "1", "2", "3", "12", "5", "40", "45", "360", "7", "112", "189", "3024", "175", "2800", "4725", "75600", "11", "352", "891", "28512", "1375", "44000", "111375", "3564000", "539", "17248", "43659", "1397088", "67375", "2156000", "5457375", "174636000", "13", "832", "3159", "202176", "8125", "520000", "1974375", "126360000", "4459", "285376", "1083537" ]
[ "nonn", "tabf", "easy", "base" ]
17
0
2
[ "A000040", "A003961", "A006939", "A007947", "A019565", "A060175", "A061395", "A071178", "A251720", "A384003" ]
null
Michael De Vlieger and Peter Munn, May 28 2025
2025-06-21T16:16:32
oeisdata/seq/A384/A384003.seq
111c18cb3f87728488c5f9bc97a78bb8
A384004
a(n) = smallest k such that A010846(k) = n.
[ "1", "2", "4", "8", "6", "10", "22", "12", "44", "18", "24", "50", "98", "36", "48", "54", "224", "30", "42", "70", "108", "66", "78", "162", "102", "60", "138", "84", "174", "260", "132", "90", "126", "228", "354", "120", "234", "168", "350", "306", "150", "516", "408", "180", "252", "552", "696", "294", "240", "336", "612", "378", "270", "1416", "300", "702", "1332", "360" ]
[ "nonn" ]
15
1
2
[ "A000079", "A001222", "A002110", "A010846", "A024619", "A162306", "A244052", "A384004" ]
null
Michael De Vlieger, Jun 10 2025
2025-06-18T00:31:33
oeisdata/seq/A384/A384004.seq
dbd6616ef1f2da01e1de5e806dca3362
A384005
Number of ways to choose disjoint strict integer partitions, one of each conjugate prime index of n.
[ "1", "1", "0", "1", "0", "1", "0", "2", "0", "0", "0", "1", "0", "0", "0", "2", "0", "1", "0", "0", "0", "0", "0", "1", "0", "0", "2", "0", "0", "1", "0", "3", "0", "0", "0", "2", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "1", "0", "0", "0", "4", "0", "0", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "0" ]
[ "nonn" ]
6
1
8
[ "A000009", "A000041", "A048767", "A048768", "A055396", "A056239", "A061395", "A098859", "A112798", "A122111", "A130091", "A179009", "A217605", "A239455", "A279375", "A279790", "A299200", "A317141", "A351293", "A351294", "A351295", "A357982", "A381432", "A381433", "A382525", "A382771", "A382913", "A383533", "A383706", "A383707", "A383708", "A383710", "A384005", "A384010", "A384011", "A384179" ]
null
Gus Wiseman, May 22 2025
2025-05-23T10:15:13
oeisdata/seq/A384/A384005.seq
c308ba9177c090c06f385f8d28c86431
A384006
Heinz numbers of Look-and-Say partitions without distinct multiplicities (non Wilf).
[ "216", "1000", "1296", "2744", "3375", "7776", "9261", "10000", "10648", "17576", "32400", "35937", "38416", "38880", "39304", "42875", "46656", "50625", "54000", "54432", "54872", "59319", "63504", "81000", "85536", "90000", "97336", "100000" ]
[ "nonn" ]
5
1
1
[ "A000720", "A001222", "A001223", "A048767", "A051903", "A055396", "A056239", "A061395", "A098859", "A112798", "A122111", "A130091", "A130092", "A212166", "A239455", "A325368", "A336866", "A351293", "A351592", "A381432", "A381433", "A383506", "A383511", "A383512", "A383513", "A383514", "A383518", "A383520", "A383531", "A384006" ]
null
Gus Wiseman, May 19 2025
2025-05-22T17:06:09
oeisdata/seq/A384/A384006.seq
11a5a8b32992114967df555ce0cadf45
A384007
Heinz numbers of non Look-and-Say section-sum partitions.
[ "10", "14", "15", "22", "26", "33", "34", "35", "38", "39", "46", "51", "55", "57", "58", "62", "65", "69", "74", "77", "82", "85", "86", "87", "91", "93", "94", "95", "100", "106", "111", "115", "118", "119", "122", "123", "129", "130", "133", "134", "141", "142", "143", "145", "146", "155", "158", "159", "161", "166", "170", "177", "178", "182", "183", "185", "187", "190" ]
[ "nonn" ]
5
1
1
[ "A000720", "A001222", "A001223", "A048767", "A048768", "A055396", "A056239", "A061395", "A098859", "A112798", "A122111", "A130091", "A212166", "A217605", "A238745", "A239455", "A325368", "A351293", "A351294", "A351295", "A381432", "A381433", "A383508", "A383509", "A383510", "A383511", "A383512", "A383514", "A383515", "A383516", "A383517", "A383518", "A383520", "A383531", "A384006", "A384007" ]
null
Gus Wiseman, May 19 2025
2025-05-22T17:06:03
oeisdata/seq/A384/A384007.seq
70a5b3f73cf5676e1929faec0388eee0
A384008
Irregular triangle read by rows where row n lists the first differences of the 0-prepended prime indices of the n-th squarefree number.
[ "1", "2", "3", "1", "1", "4", "1", "2", "5", "6", "1", "3", "2", "1", "7", "8", "2", "2", "1", "4", "9", "1", "5", "10", "1", "1", "1", "11", "2", "3", "1", "6", "3", "1", "12", "1", "7", "2", "4", "13", "1", "1", "2", "14", "1", "8", "15", "2", "5", "16", "3", "2", "2", "6", "1", "9", "17", "18", "1", "10", "3", "3", "1", "1", "3", "19", "2", "7", "1", "2", "1", "20", "21", "1", "11", "4", "1", "1", "1", "4", "22", "1", "12", "23", "3", "4" ]
[ "nonn", "tabf" ]
5
1
2
[ "A000040", "A001221", "A001222", "A001223", "A005117", "A048767", "A055396", "A056239", "A061395", "A072047", "A112798", "A243290", "A320348", "A325324", "A325325", "A325367", "A325388", "A351294", "A351295", "A355536", "A358137", "A383534", "A383535", "A384008", "A384009" ]
null
Gus Wiseman, May 23 2025
2025-05-23T10:15:08
oeisdata/seq/A384/A384008.seq
31cb110077468d026c0877c0a34d492e
A384009
Irregular triangle read by rows where row n lists the positive first differences of the prime indices of n.
[ "1", "2", "1", "3", "1", "1", "2", "2", "4", "1", "5", "3", "1", "1", "3", "6", "1", "1", "7", "4", "2", "1", "2", "4", "1", "8", "1", "2", "5", "5", "1", "2", "3", "6", "9", "1", "1", "10", "2", "3", "1", "3", "6", "7", "2", "1", "1", "11", "1", "7", "1", "1", "4", "2", "12", "1", "2", "4", "13", "8", "4", "1", "1", "2", "8", "9", "14", "5", "1", "3", "3", "2", "1", "5", "5", "1", "1", "15", "1", "2", "2", "10", "3", "1", "6", "6" ]
[ "nonn", "tabf" ]
6
1
2
[ "A000040", "A001221", "A001222", "A001223", "A039956", "A048767", "A055396", "A056239", "A061395", "A112798", "A124010", "A130091", "A243055", "A287352", "A320348", "A325325", "A325349", "A325368", "A325992", "A355536", "A358137", "A381431", "A383534", "A384009" ]
null
Gus Wiseman, May 23 2025
2025-05-23T10:15:03
oeisdata/seq/A384/A384009.seq
374fc719638d8a47b15dba213881fb20
A384010
Heinz numbers of integer partitions such that it is possible to choose a family of disjoint strict partitions, one of each conjugate part.
[ "1", "2", "4", "6", "8", "12", "16", "18", "24", "27", "30", "32", "36", "48", "54", "60", "64", "72", "81", "90", "96", "108", "120", "128", "144", "150", "162", "180", "192" ]
[ "nonn", "more" ]
10
1
2
[ "A000009", "A000041", "A048767", "A048768", "A055396", "A056239", "A061395", "A098859", "A112798", "A122111", "A130091", "A217605", "A239455", "A279375", "A279790", "A299200", "A351293", "A351294", "A351295", "A357982", "A381432", "A381433", "A382525", "A382912", "A383533", "A383706", "A383707", "A383708", "A383710", "A383711", "A384005", "A384010", "A384011" ]
null
Gus Wiseman, May 23 2025
2025-05-24T11:00:35
oeisdata/seq/A384/A384010.seq
00c53e30b5f113b13fcf8b9af4276c38
A384011
Numbers k such that it is not possible to choose disjoint strict integer partitions of each conjugate prime index of k.
[ "3", "5", "7", "9", "10", "11", "13", "14", "15", "17", "19", "20", "21", "22", "23", "25", "26", "28", "29", "31", "33", "34", "35", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46", "47", "49", "50", "51", "52", "53", "55", "56", "57", "58", "59", "61", "62", "63", "65", "66", "67", "68", "69", "70", "71", "73", "74", "75", "76", "77", "78", "79", "80", "82", "83", "84", "85" ]
[ "nonn" ]
12
1
1
[ "A000009", "A000041", "A048767", "A048768", "A055396", "A056239", "A061395", "A098859", "A112798", "A122111", "A130091", "A217605", "A239455", "A279375", "A279790", "A351293", "A351294", "A351295", "A357982", "A381432", "A381433", "A382525", "A382912", "A382913", "A383533", "A383706", "A383707", "A383708", "A383710", "A383711", "A384005", "A384010", "A384011" ]
null
Gus Wiseman, May 23 2025
2025-06-08T14:20:12
oeisdata/seq/A384/A384011.seq
145bec307376cd9c6a0b255974fc443c
A384012
a(n) = [x^n] Product_{k=0..n} (1 + k*x)^3.
[ "1", "3", "33", "630", "17247", "616770", "27264976", "1436603616", "87922855935", "6131105251425", "479931312805425", "41674568874964740", "3975727750503656820", "413360925414308633034", "46523118781014280909560", "5635356193271621706436800", "730994763063708819170060751", "101099888222006502307905386445" ]
[ "nonn" ]
22
0
2
[ "A129256", "A351507", "A383862", "A384012", "A384017", "A384031" ]
null
Seiichi Manyama, May 17 2025
2025-05-19T04:55:58
oeisdata/seq/A384/A384012.seq
533ab5461760607800658ab7b962c85e
A384013
Primes with at least two identical leading digits.
[ "11", "113", "223", "227", "229", "331", "337", "443", "449", "557", "661", "773", "881", "883", "887", "991", "997", "1103", "1109", "1117", "1123", "1129", "1151", "1153", "1163", "1171", "1181", "1187", "1193", "2203", "2207", "2213", "2221", "2237", "2239", "2243", "2251", "2267", "2269", "2273", "2281", "2287", "2293", "2297", "3301", "3307", "3313" ]
[ "nonn", "base" ]
9
1
1
[ "A050758", "A062353", "A383978", "A384013", "A384014", "A384015" ]
null
Stefano Spezia, May 17 2025
2025-05-20T00:20:57
oeisdata/seq/A384/A384013.seq
d042438aa31c567eface63ad92bf654a
A384014
a(n) is the number of n-digit terms in A384013.
[ "0", "1", "16", "108", "834", "6893", "58659", "510839", "4515301", "40477023", "366751460", "3352789726", "30877698604", "286159371452", "2666303391801", "24959756192476", "234610874384116", "2213224276178123", "20945897352118544", "198802912201260034", "1891788092230264832", "18044365524165259927", "172479703095316537972" ]
[ "nonn", "base" ]
15
1
3
[ "A383979", "A384013", "A384014", "A384016" ]
null
Stefano Spezia, May 17 2025
2025-05-20T11:48:24
oeisdata/seq/A384/A384014.seq
fe27cba5be315502f2e2f24016723401
A384015
Primes with at least two identical trailing digits and at least two identical leading digits.
[ "11", "11177", "11299", "11311", "11399", "11411", "11633", "11677", "11699", "11777", "11833", "11933", "22111", "22133", "22277", "22433", "22511", "22699", "22777", "22811", "22877", "33199", "33211", "33311", "33377", "33533", "33577", "33599", "33811", "33911", "44111", "44533", "44633", "44699", "44711", "44777", "55333", "55399" ]
[ "nonn", "base" ]
11
1
1
[ "A050758", "A383978", "A384013", "A384015", "A384016" ]
null
Stefano Spezia, May 17 2025
2025-05-20T15:48:29
oeisdata/seq/A384/A384015.seq
833a6aab20dbd35ec415700f1f2ebf77
A384016
a(n) is the number of n-digit terms in A384015.
[ "0", "1", "0", "0", "74", "673", "5851", "50977", "451608", "4048657", "36675547", "335269867", "3087739250", "28615970101" ]
[ "nonn", "base", "more" ]
22
1
5
[ "A383979", "A384014", "A384015", "A384016" ]
null
Stefano Spezia, May 17 2025
2025-05-22T09:35:04
oeisdata/seq/A384/A384016.seq
2def1b86393f92a3630f9d6a1dbd6e79
A384017
a(n) = [x^n] Product_{k=0..n} (1 + k*x)^5.
[ "1", "5", "100", "3510", "177370", "11732175", "960453825", "93791830160", "10644367637490", "1376936603007075", "200002385378370350", "32233130183113838550", "5708169533474858008905", "1101836121788665346133960", "230256048227047074266497400", "51791322674249971562728368000" ]
[ "nonn" ]
42
0
2
[ "A000142", "A129256", "A351507", "A384012", "A384017", "A384031" ]
null
Seiichi Manyama, May 18 2025
2025-05-19T04:35:45
oeisdata/seq/A384/A384017.seq
138a463a4984156bc43cb61f23730ce7
A384018
a(n) = [x^n] Product_{k=0..n-1} (1 + k*x)^3.
[ "1", "0", "3", "63", "1767", "63690", "2822740", "148810032", "9104502015", "634448680884", "49622704133175", "4305280182748875", "410376649359397380", "42633179822414174760", "4794685285831034253660", "580373328155358031572600", "75234419898396217903091151", "10398952352945773993329785448", "1526704288048697734221906020641" ]
[ "nonn" ]
10
0
3
[ "A342111", "A384018", "A384026", "A384029" ]
null
Seiichi Manyama, May 17 2025
2025-05-17T14:02:05
oeisdata/seq/A384/A384018.seq
d5b3139d4a1dc02bf38acf1e5d9a18fb
A384019
a(n) = [x^n] Product_{k=0..n-1} 1/(1 - k*x)^3.
[ "1", "0", "6", "198", "8718", "493620", "34379705", "2848881861", "274014843102", "30021594006888", "3692052527349420", "503688013660560300", "75497500934983279207", "12333902414342152783230", "2181353542325197013657520", "415235853517370112251703000", "84651012612907530893554863870", "18400893142622338322496213279696", "4248568325843735030714223895999412" ]
[ "nonn" ]
7
0
3
[ "A384019", "A384023" ]
null
Seiichi Manyama, May 17 2025
2025-05-17T13:59:31
oeisdata/seq/A384/A384019.seq
6a87a06a51a000601224ed9d2486230e
A384020
Numbers k > 0 such that sigma(A018804(k)) = k*tau(A018804(k)) where sigma denotes the sum of divisors (A000203) and tau denotes the number of divisors (A000005).
[ "1", "2", "3", "6", "7", "10", "14", "19", "21", "30", "31", "37", "38", "39", "42", "57", "62", "70", "74", "78", "79", "93", "97", "111", "114", "133", "139", "157", "158", "186", "190", "194", "199", "210", "211", "217", "222", "229", "237", "259", "266", "271", "273", "278", "291", "307", "310", "314", "331", "337", "367", "370", "379", "390", "398", "399", "410" ]
[ "nonn" ]
14
1
2
[ "A000005", "A000203", "A018804", "A382872", "A384020" ]
null
Ctibor O. Zizka, May 17 2025
2025-05-28T23:31:54
oeisdata/seq/A384/A384020.seq
96c0b17c9f593d1e7aefbbe2ff9e4d65
A384021
Powers of 2 along with numbers one power of 2 less than binary repunits, but the power of two subtracted does not flip the leading bit.
[ "1", "2", "4", "5", "6", "8", "11", "13", "14", "16", "23", "27", "29", "30", "32", "47", "55", "59", "61", "62", "64", "95", "111", "119", "123", "125", "126", "128", "191", "223", "239", "247", "251", "253", "254", "256", "383", "447", "479", "495", "503", "507", "509", "510", "512", "767", "895", "959", "991", "1007", "1015", "1019", "1021", "1022", "1024", "1535", "1791", "1919" ]
[ "nonn", "base", "easy" ]
43
1
2
[ "A000079", "A030130", "A164874", "A383666", "A384021" ]
null
David A. Corneth, May 17 2025
2025-06-13T08:20:28
oeisdata/seq/A384/A384021.seq
f9f230fe9a2c82bfcd6c6ccba7115fc0
A384022
a(n) = [x^(2*n)] Product_{k=0..n} 1/(1 - k*x)^3.
[ "1", "6", "699", "242434", "170580831", "202617635850", "364680579642546", "926271490234962816", "3156974021179142865351", "13905988122027295313489800", "76896867190774672671251191752", "521595538342870729288480053506382", "4258687803431080424982372253063299050", "41202042785933045982333959380025893914894" ]
[ "nonn" ]
13
0
2
[ "A383862", "A384022" ]
null
Seiichi Manyama, May 17 2025
2025-05-22T05:27:33
oeisdata/seq/A384/A384022.seq
c8ef6de56639242bdfdcbe373675fbfd
A384023
a(n) = [x^(2*n)] Product_{k=0..n-1} 1/(1 - k*x)^3.
[ "1", "0", "15", "6562", "5011791", "6200184825", "11429262789510", "29485293941863746", "101592807373290699207", "451093709664199690854238", "2509724586752840748604036752", "17105620782434790456521322932280", "140205097075941134305471628610608762", "1360788914644085139603907391284501566930" ]
[ "nonn" ]
8
0
3
[ "A384019", "A384023" ]
null
Seiichi Manyama, May 17 2025
2025-05-17T14:00:05
oeisdata/seq/A384/A384023.seq
f60d5639690ce0ddc7ef08f08414f1ba
A384024
a(n) = [x^n] Product_{k=0..n} (1 + (n+k)*x).
[ "1", "3", "26", "342", "5944", "127860", "3272688", "97053936", "3270729600", "123418922400", "5154170774400", "235977273544320", "11752173128586240", "632474276804697600", "36576553723886131200", "2261980049125982976000", "148956705206745595084800", "10406288081667512679321600", "768701832940487804295168000" ]
[ "nonn" ]
19
0
2
[ "A000407", "A165675", "A201546", "A383869", "A384024" ]
null
Vaclav Kotesovec, May 17 2025
2025-05-18T09:58:09
oeisdata/seq/A384/A384024.seq
1c3644ffa1ffb071e0da4bd2cc3718ff
A384025
a(n) = [x^(2*n)] Product_{k=0..n} (1 + k*x)^3.
[ "1", "3", "66", "3815", "424428", "77530530", "21106440064", "8021533034676", "4060456997959152", "2642189599046492000", "2149789283054191431744", "2139041823964877704864992", "2555760236856152336740829440", "3611539707805518014521602175296", "5958533262158042791156143146398464" ]
[ "nonn" ]
13
0
2
[ "A129256", "A382925", "A384025" ]
null
Seiichi Manyama, May 17 2025
2025-05-22T11:58:59
oeisdata/seq/A384/A384025.seq
fc11d4ba2d9441cda07b0004d3d5b69d
A384026
a(n) = [x^(2*n)] Product_{k=0..n-1} (1 + k*x)^3.
[ "1", "0", "0", "8", "1188", "240480", "68630824", "26730127872", "13715719388784", "8994742935058880", "7351374493516431744", "7333037983443263351040", "8772990646534399559904256", "12403600039078715891159873280", "20464777911173655904724421045504", "38976211807455406964301439206318080" ]
[ "nonn" ]
10
0
4
[ "A342111", "A384018", "A384026", "A384027" ]
null
Seiichi Manyama, May 17 2025
2025-05-17T14:01:50
oeisdata/seq/A384/A384026.seq
38a32c41196df5e1a383435aa99de444
A384027
a(n) = [x^(3*n)] Product_{k=0..n-1} (1 + k*x)^4.
[ "1", "0", "0", "0", "1296", "2764800", "8041766400", "34726710251520", "219045033712578816", "1956771788423009992704", "24009126017002632247173120", "393692515265172002272138690560", "8424620140673205407840209386541056", "230472036551670538296109810120063451136", "7917891968134805796965854747528387122954240" ]
[ "nonn" ]
9
0
5
[ "A342111", "A384026", "A384027", "A384029", "A384030" ]
null
Seiichi Manyama, May 17 2025
2025-05-17T14:01:39
oeisdata/seq/A384/A384027.seq
2405ff4106485acbcd2f31feb8997d61
A384028
a(n) = Sum_{k=0..2*n} Stirling1(2*n+1, 2*n+1-k) * Stirling1(2*n+1, k+1).
[ "1", "13", "2273", "1184153", "1251320145", "2232012515445", "6032418472347265", "23007314730623658225", "117745011140615270168865", "778780810721500176081199325", "6466413475830749109197652489569", "65861328745485785925705177696147337", "807448787241269228642562251336079833585" ]
[ "nonn" ]
12
0
2
[ "A129256", "A234324", "A384028" ]
null
Vaclav Kotesovec, May 17 2025
2025-05-17T13:58:32
oeisdata/seq/A384/A384028.seq
e4e6448fd5dbe52f6087c8904e1f968e
A384029
a(n) = [x^n] Product_{k=0..n-1} (1 + k*x)^4.
[ "1", "0", "6", "180", "7206", "370880", "23477380", "1768061064", "154544373158", "15387101825184", "1719596420272980", "213181689525888600", "29036623040055512332", "4310582688852993653568", "692756995680614782818992", "119830419866883597939018000", "22198322332579642585088580870", "4384714751330840129324051474880" ]
[ "nonn" ]
10
0
3
[ "A342111", "A384018", "A384027", "A384029", "A384030", "A384031" ]
null
Seiichi Manyama, May 17 2025
2025-05-17T14:00:56
oeisdata/seq/A384/A384029.seq
dfac2d50adfadf1e754ba6d3e2549273
A384030
a(n) = [x^(2*n)] Product_{k=0..n-1} (1 + k*x)^4.
[ "1", "0", "1", "248", "79441", "38878520", "27741179521", "27412462941136", "35965398129639713", "60588665662486807184", "127588718827126433989569", "328596587850349392471155720", "1016488989627693108972046560497", "3720090951049096346043302894560648", "15901046580509525131539058273675597889" ]
[ "nonn" ]
9
0
4
[ "A384027", "A384029", "A384030" ]
null
Seiichi Manyama, May 17 2025
2025-05-17T14:01:08
oeisdata/seq/A384/A384030.seq
6d483d6566080e0b6edf4287e20c18e8
A384031
a(n) = [x^n] Product_{k=0..n} (1 + k*x)^4.
[ "1", "4", "62", "1680", "65446", "3334800", "210218956", "15803243456", "1380404187558", "137419388080920", "15359405910256580", "1904647527097204032", "259511601503239509004", "38539384808775589973416", "6195988524478342471690200", "1072149116496356641327200000", "198683315255720972000976370950" ]
[ "nonn" ]
19
0
2
[ "A129256", "A351507", "A382925", "A384012", "A384017", "A384029", "A384031", "A384032", "A384060" ]
null
Seiichi Manyama, May 17 2025
2025-05-19T04:54:48
oeisdata/seq/A384/A384031.seq
7a26aecde934d90b9533a55d01fffb34
A384032
a(n) = [x^(2*n)] Product_{k=0..n} (1 + k*x)^4.
[ "1", "6", "321", "46364", "13052881", "6077950570", "4237586784577", "4137911590389080", "5394217192300621089", "9055251708372687577550", "19032397641903957029149569", "48970167155426122072661229684", "151429299992138418402024853511537", "554184682895238619253412365302575346" ]
[ "nonn" ]
15
0
2
[ "A382925", "A384031", "A384032" ]
null
Seiichi Manyama, May 17 2025
2025-05-22T13:20:38
oeisdata/seq/A384/A384032.seq
07aaabb1d09075212578493b025372b4
A384033
a(n) is the number of solutions to n = sopfr(k*sopfr(n)) where sopfr(m) is sum of prime factors of m counted with multiplicity.
[ "0", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "2", "1", "3", "4", "5", "1", "7", "1", "10", "10", "4", "1", "19", "19", "19", "30", "17", "1", "40", "1", "52", "46", "12", "77", "87", "1", "77", "111", "87", "1", "175", "1", "197", "157", "197", "1", "219", "302", "413", "372", "175", "1", "413", "614", "413", "456", "67", "1", "1083", "1", "677", "819", "1552", "1552", "1695", "1" ]
[ "nonn", "new" ]
48
1
12
[ "A000607", "A001414", "A384033" ]
null
Michael Terhoeven, May 17 2025
2025-07-02T00:55:06
oeisdata/seq/A384/A384033.seq
704186b81a3f05a6db165219fbad92a9
A384034
Irregular triangle read by rows. Start with T(1,1) = 1. For each subsequent row, traverse the array so far. For each value m, insert m new values from the next unused integers immediately to the right of m. The process is repeated row by row, where each number in the array dictates how many new values are added after it.
[ "1", "1", "2", "1", "3", "2", "4", "5", "1", "6", "3", "7", "8", "9", "2", "10", "11", "4", "12", "13", "14", "15", "5", "16", "17", "18", "19", "20", "1", "21", "6", "22", "23", "24", "25", "26", "27", "3", "28", "29", "30", "7", "31", "32", "33", "34", "35", "36", "37", "8", "38", "39", "40", "41", "42", "43", "44", "45", "9", "46", "47", "48", "49", "50", "51", "52", "53", "54", "2", "55", "56" ]
[ "nonn", "tabf" ]
27
1
3
null
null
Ali Sada, May 21 2025
2025-06-04T10:24:47
oeisdata/seq/A384/A384034.seq
b31af0f586ab2f97dcebea402448b5af
A384035
Number of vector differences between two permutations of order n, up to multiplication by positive rational numbers and permutations of the components.
[ "1", "1", "2", "4", "13", "49", "228", "1034", "5133", "25710", "133872", "708976", "3846150", "21170077", "118429072", "670537495" ]
[ "nonn", "more", "hard" ]
6
0
3
[ "A019589", "A175176", "A362968", "A381243", "A381244", "A381339", "A384035" ]
null
Max Alekseyev, May 17 2025
2025-05-18T02:30:36
oeisdata/seq/A384/A384035.seq
58df9ef1024fe8ccb7aa3a8a09259955
A384036
Decimal expansion of the surface area of a regular pentagonal prism of edge length 1.
[ "8", "4", "4", "0", "9", "5", "4", "8", "0", "1", "1", "7", "7", "9", "3", "3", "8", "4", "5", "5", "1", "8", "0", "2", "3", "9", "5", "4", "7", "7", "7", "2", "1", "9", "1", "9", "8", "8", "1", "4", "7", "4", "8", "3", "4", "0", "0", "2", "0", "3", "9", "6", "6", "5", "8", "4", "1", "4", "1", "8", "9", "4", "1", "4", "0", "4", "7", "7", "3", "7", "9", "8", "4", "4", "1", "7", "9", "3", "2", "4", "6", "2", "6", "6", "4", "8", "8" ]
[ "nonn", "cons" ]
28
1
1
[ "A102771", "A178809", "A300074", "A384036", "A384059" ]
null
Kritsada Moomuang, May 17 2025
2025-05-22T19:08:12
oeisdata/seq/A384/A384036.seq
8db17a363c112ae98b363cd379efd7d8
A384037
Number of paths with length A383980(n) touching all cells in an n X n grid, where rotations, reflections, and translations are not counted as distinct.
[ "1", "1", "1", "1", "1", "1", "3", "6", "3", "9", "42" ]
[ "nonn", "more", "hard", "walk" ]
14
0
7
[ "A383980", "A384037" ]
null
Fülöp Tamás, May 17 2025
2025-05-18T12:28:02
oeisdata/seq/A384/A384037.seq
a90f4b4490a2c57f54ffd43fcb9b36a6
A384038
Number of 2n X 2n matrices M over GF(2) such that the column space of M is equal to the null space of M.
[ "1", "3", "210", "234360", "4047865920", "1092146608143360", "4650098142288472473600", "314462403262051153026062745600", "338960040818652280796119613717033779200", "5834618256563872511581456247120956565738854809600", "1605370810586153268821245248112723240374305354675084328960000" ]
[ "nonn" ]
15
0
2
[ "A002884", "A006098", "A053763", "A346214", "A384038" ]
null
Geoffrey Critzer, May 17 2025
2025-05-18T07:57:20
oeisdata/seq/A384/A384038.seq
9ceace2345cf9448b7960fb977c1d104
A384039
The number of integers k from 1 to n such that gcd(n,k) is a powerful number.
[ "1", "1", "2", "3", "4", "2", "6", "6", "7", "4", "10", "6", "12", "6", "8", "12", "16", "7", "18", "12", "12", "10", "22", "12", "21", "12", "21", "18", "28", "8", "30", "24", "20", "16", "24", "21", "36", "18", "24", "24", "40", "12", "42", "30", "28", "22", "46", "24", "43", "21", "32", "36", "52", "21", "40", "36", "36", "28", "58", "24", "60", "30", "42", "48", "48", "20", "66", "48", "44" ]
[ "nonn", "easy", "mult" ]
12
1
3
[ "A000010", "A001694", "A005117", "A026741", "A050873", "A055231", "A062570", "A063658", "A063659", "A078429", "A116512", "A117494", "A126246", "A206369", "A254926", "A372671", "A384039", "A384040", "A384041", "A384042" ]
null
Amiram Eldar, May 18 2025
2025-05-18T04:34:21
oeisdata/seq/A384/A384039.seq
b3238b20481fa53b3d61cfc1d8fc00b7
A384040
The number of integers k from 1 to n such that gcd(n,k) is a cubefull number.
[ "1", "1", "2", "2", "4", "2", "6", "5", "6", "4", "10", "4", "12", "6", "8", "10", "16", "6", "18", "8", "12", "10", "22", "10", "20", "12", "19", "12", "28", "8", "30", "20", "20", "16", "24", "12", "36", "18", "24", "20", "40", "12", "42", "20", "24", "22", "46", "20", "42", "20", "32", "24", "52", "19", "40", "30", "36", "28", "58", "16", "60", "30", "36", "40", "48", "20", "66", "32", "44", "24" ]
[ "nonn", "easy", "mult" ]
7
1
3
[ "A005117", "A026741", "A036966", "A062570", "A063659", "A078429", "A116512", "A117494", "A126246", "A206369", "A254926", "A360539", "A372671", "A384039", "A384040", "A384041", "A384042" ]
null
Amiram Eldar, May 18 2025
2025-05-18T04:24:26
oeisdata/seq/A384/A384040.seq
04b1979f2306f799f4c109f62e125be2
A384041
The number of integers k from 1 to n such that gcd(n,k) is an exponentially odd number.
[ "1", "2", "3", "3", "5", "6", "7", "7", "8", "10", "11", "9", "13", "14", "15", "13", "17", "16", "19", "15", "21", "22", "23", "21", "24", "26", "25", "21", "29", "30", "31", "27", "33", "34", "35", "24", "37", "38", "39", "35", "41", "42", "43", "33", "40", "46", "47", "39", "48", "48", "51", "39", "53", "50", "55", "49", "57", "58", "59", "45", "61", "62", "56", "53", "65", "66", "67", "51" ]
[ "nonn", "easy", "mult" ]
7
1
2
[ "A000010", "A026741", "A062570", "A063659", "A078429", "A116512", "A117494", "A126246", "A206369", "A254926", "A268335", "A372671", "A384039", "A384040", "A384041", "A384042" ]
null
Amiram Eldar, May 18 2025
2025-05-18T04:29:34
oeisdata/seq/A384/A384041.seq
197d75421aad6bef206d09d6639da3ae
A384042
The number of integers k from 1 to n such that gcd(n,k) is a 5-rough number (A007310).
[ "1", "1", "2", "2", "5", "2", "7", "4", "6", "5", "11", "4", "13", "7", "10", "8", "17", "6", "19", "10", "14", "11", "23", "8", "25", "13", "18", "14", "29", "10", "31", "16", "22", "17", "35", "12", "37", "19", "26", "20", "41", "14", "43", "22", "30", "23", "47", "16", "49", "25", "34", "26", "53", "18", "55", "28", "38", "29", "59", "20", "61", "31", "42", "32", "65", "22", "67", "34", "46" ]
[ "nonn", "easy", "mult" ]
9
1
3
[ "A000010", "A003586", "A007310", "A026741", "A062570", "A063659", "A065330", "A065331", "A078429", "A116512", "A117494", "A126246", "A206369", "A254926", "A372671", "A384039", "A384040", "A384041", "A384042" ]
null
Amiram Eldar, May 18 2025
2025-05-25T12:36:39
oeisdata/seq/A384/A384042.seq
1cecc39386917a021d4a59c413af7060
A384043
a(n) = [x^n] Product_{k=1..n} (1 + k^2*x) / (1 - k^2*x).
[ "1", "2", "50", "4188", "735600", "221302710", "101667388082", "66218673102680", "58048466179356672", "65901249246347377770", "94061755750395244537250", "164863945136411230998746612", "348110204753572939058548570000", "871547135491620353615820806025918", "2552918049709989779004770502542335650" ]
[ "nonn" ]
5
0
2
[ "A001044", "A298851", "A350366", "A351764", "A384043", "A384044" ]
null
Vaclav Kotesovec, May 18 2025
2025-05-18T04:10:05
oeisdata/seq/A384/A384043.seq
7bbfe3d7db783bf9e2c879e012b75f77
A384044
a(n) = [x^n] Product_{k=1..n} (1 + k^3*x) / (1 - k^3*x).
[ "1", "2", "162", "75672", "104312000", "317309605650", "1803288012589602", "17180843554017736544", "254292459616733559570432", "5525508321588276184345621650", "168733575675064578625834983478850", "6994229599670887851052241626545021912", "382562895157136117988572795915676719695680" ]
[ "nonn" ]
4
0
2
[ "A000442", "A350366", "A351764", "A351800", "A384043", "A384044" ]
null
Vaclav Kotesovec, May 18 2025
2025-05-18T04:09:59
oeisdata/seq/A384/A384044.seq
3ea5bb8384531f4cb17804affac275b2
A384045
a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest unused positive number that shares a factor with a(n-1) if it is greater than it, else it is coprime to a(n-1) if it is less than it.
[ "1", "2", "4", "3", "6", "5", "10", "7", "14", "9", "8", "12", "11", "22", "13", "26", "15", "18", "17", "16", "20", "19", "38", "21", "24", "23", "46", "25", "30", "29", "27", "33", "28", "32", "31", "62", "35", "34", "36", "39", "37", "74", "41", "40", "42", "44", "43", "86", "45", "48", "47", "94", "49", "56", "51", "50", "52", "54", "53", "106", "55", "60", "59", "57", "63", "58", "64", "61" ]
[ "nonn" ]
13
1
2
[ "A064413", "A373545", "A373546", "A375563", "A375564", "A384045" ]
null
Scott R. Shannon, May 18 2025
2025-05-27T10:34:43
oeisdata/seq/A384/A384045.seq
27e3e3be9de4593b52aa30bf20b6abae
A384046
Triangle in which the n-th row gives the numbers from 1 to n whose largest divisor that is a unitary divisor of n is 1.
[ "1", "1", "1", "2", "1", "2", "3", "1", "2", "3", "4", "1", "5", "1", "2", "3", "4", "5", "6", "1", "2", "3", "4", "5", "6", "7", "1", "2", "3", "4", "5", "6", "7", "8", "1", "3", "7", "9", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "1", "2", "5", "7", "10", "11", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "1", "3", "5", "9", "11", "13", "1", "2", "4", "7", "8", "11", "13", "14", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15" ]
[ "nonn", "tabf", "easy" ]
12
1
4
[ "A038566", "A047994", "A077610", "A225174", "A333576", "A384046", "A384047" ]
null
Amiram Eldar, May 18 2025
2025-05-24T03:32:22
oeisdata/seq/A384/A384046.seq
b33d27ede964a286a8b664a0f640b9f0
A384047
Triangle read by rows: T(n, k) for 1 <= k <= n is the largest divisor of k that is a unitary divisor of n.
[ "1", "1", "2", "1", "1", "3", "1", "1", "1", "4", "1", "1", "1", "1", "5", "1", "2", "3", "2", "1", "6", "1", "1", "1", "1", "1", "1", "7", "1", "1", "1", "1", "1", "1", "1", "8", "1", "1", "1", "1", "1", "1", "1", "1", "9", "1", "2", "1", "2", "5", "2", "1", "2", "1", "10", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "11", "1", "1", "3", "4", "1", "3", "1", "4", "3", "1", "1", "12", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "13" ]
[ "nonn", "tabl", "easy" ]
11
1
3
[ "A005117", "A050873", "A077610", "A145388", "A165430", "A225174", "A322482", "A384046", "A384047" ]
null
Amiram Eldar, May 18 2025
2025-05-24T03:32:26
oeisdata/seq/A384/A384047.seq
46485c9ffb5c2f496daf5ac6436b6879
A384048
The number of integers k from 1 to n such that the greatest divisor of k that is a unitary divisor of n is squarefree.
[ "1", "2", "3", "3", "5", "6", "7", "7", "8", "10", "11", "9", "13", "14", "15", "15", "17", "16", "19", "15", "21", "22", "23", "21", "24", "26", "26", "21", "29", "30", "31", "31", "33", "34", "35", "24", "37", "38", "39", "35", "41", "42", "43", "33", "40", "46", "47", "45", "48", "48", "51", "39", "53", "52", "55", "49", "57", "58", "59", "45", "61", "62", "56", "63", "65", "66", "67", "51" ]
[ "nonn", "easy", "mult" ]
11
1
2
[ "A000010", "A005117", "A047994", "A055231", "A057521", "A063659", "A065466", "A384046", "A384047", "A384048", "A384049", "A384050", "A384051", "A384052", "A384053", "A384054", "A384055", "A384056", "A384057", "A384058" ]
null
Amiram Eldar, May 18 2025
2025-05-21T01:32:16
oeisdata/seq/A384/A384048.seq
17774ce0c94e2d3255970b288723ccc2
A384049
The number of integers k from 1 to n such that the greatest divisor of k that is a unitary divisor of n is cubefree.
[ "1", "2", "3", "4", "5", "6", "7", "7", "9", "10", "11", "12", "13", "14", "15", "15", "17", "18", "19", "20", "21", "22", "23", "21", "25", "26", "26", "28", "29", "30", "31", "31", "33", "34", "35", "36", "37", "38", "39", "35", "41", "42", "43", "44", "45", "46", "47", "45", "49", "50", "51", "52", "53", "52", "55", "49", "57", "58", "59", "60", "61", "62", "63", "63", "65", "66", "67", "68" ]
[ "nonn", "easy", "mult" ]
10
1
2
[ "A004709", "A047994", "A065468", "A254926", "A360539", "A360540", "A384046", "A384047", "A384048", "A384049", "A384050", "A384051", "A384052", "A384053", "A384054", "A384055", "A384056", "A384057", "A384058" ]
null
Amiram Eldar, May 18 2025
2025-05-21T01:32:09
oeisdata/seq/A384/A384049.seq
8e709e48ea0225fa815577ec698ed676
A384050
The number of integers k from 1 to n such that the greatest divisor of k that is a unitary divisor of n is a powerful number.
[ "1", "1", "2", "4", "4", "2", "6", "8", "9", "4", "10", "8", "12", "6", "8", "16", "16", "9", "18", "16", "12", "10", "22", "16", "25", "12", "27", "24", "28", "8", "30", "32", "20", "16", "24", "36", "36", "18", "24", "32", "40", "12", "42", "40", "36", "22", "46", "32", "49", "25", "32", "48", "52", "27", "40", "48", "36", "28", "58", "32", "60", "30", "54", "64", "48", "20", "66", "64", "44" ]
[ "nonn", "easy", "mult" ]
10
1
3
[ "A000010", "A001694", "A047994", "A055231", "A057521", "A330596", "A384039", "A384046", "A384047", "A384048", "A384049", "A384050", "A384051", "A384052", "A384053", "A384054", "A384055", "A384056", "A384057", "A384058" ]
null
Amiram Eldar, May 18 2025
2025-05-21T01:32:21
oeisdata/seq/A384/A384050.seq
b042620b797b0dfe16222b5e0e887962
A384051
The number of integers k from 1 to n such that the greatest divisor of k that is a unitary divisor of n is a cubefull number.
[ "1", "1", "2", "3", "4", "2", "6", "8", "8", "4", "10", "6", "12", "6", "8", "16", "16", "8", "18", "12", "12", "10", "22", "16", "24", "12", "27", "18", "28", "8", "30", "32", "20", "16", "24", "24", "36", "18", "24", "32", "40", "12", "42", "30", "32", "22", "46", "32", "48", "24", "32", "36", "52", "27", "40", "48", "36", "28", "58", "24", "60", "30", "48", "64", "48", "20", "66", "48", "44" ]
[ "nonn", "easy", "mult" ]
10
1
3
[ "A036966", "A047994", "A360539", "A360540", "A384040", "A384046", "A384047", "A384048", "A384049", "A384050", "A384051", "A384052", "A384053", "A384054", "A384055", "A384056", "A384057", "A384058" ]
null
Amiram Eldar, May 18 2025
2025-05-21T01:33:29
oeisdata/seq/A384/A384051.seq
c901314bedeea2d757cb1339d4a9d2d6
A384052
The number of integers k from 1 to n such that the greatest divisor of k that is a unitary divisor of n is a square.
[ "1", "1", "2", "4", "4", "2", "6", "7", "9", "4", "10", "8", "12", "6", "8", "16", "16", "9", "18", "16", "12", "10", "22", "14", "25", "12", "26", "24", "28", "8", "30", "31", "20", "16", "24", "36", "36", "18", "24", "28", "40", "12", "42", "40", "36", "22", "46", "32", "49", "25", "32", "48", "52", "26", "40", "42", "36", "28", "58", "32", "60", "30", "54", "64", "48", "20", "66", "64", "44" ]
[ "nonn", "easy", "mult" ]
8
1
3
[ "A013662", "A047994", "A206369", "A350388", "A350389", "A384046", "A384047", "A384048", "A384049", "A384050", "A384051", "A384052", "A384053", "A384054", "A384055", "A384056", "A384057", "A384058" ]
null
Amiram Eldar, May 18 2025
2025-05-21T01:32:27
oeisdata/seq/A384/A384052.seq
cef07b7846fc5bc5ee095ced60bd766f
A384053
The number of integers k from 1 to n such that the greatest divisor of k that is a unitary divisor of n is a cube.
[ "1", "1", "2", "3", "4", "2", "6", "8", "8", "4", "10", "6", "12", "6", "8", "15", "16", "8", "18", "12", "12", "10", "22", "16", "24", "12", "27", "18", "28", "8", "30", "31", "20", "16", "24", "24", "36", "18", "24", "32", "40", "12", "42", "30", "32", "22", "46", "30", "48", "24", "32", "36", "52", "27", "40", "48", "36", "28", "58", "24", "60", "30", "48", "64", "48", "20", "66", "48", "44" ]
[ "nonn", "easy", "mult" ]
8
1
3
[ "A013664", "A047994", "A078429", "A384046", "A384047", "A384048", "A384049", "A384050", "A384051", "A384052", "A384053", "A384054", "A384055", "A384056", "A384057", "A384058" ]
null
Amiram Eldar, May 18 2025
2025-05-21T01:33:24
oeisdata/seq/A384/A384053.seq
c170cffdc706b8f409ebc99afe645ca1
A384054
The number of integers k from 1 to n such that the greatest divisor of k that is a unitary divisor of n is an exponentially odd number.
[ "1", "2", "3", "3", "5", "6", "7", "8", "8", "10", "11", "9", "13", "14", "15", "15", "17", "16", "19", "15", "21", "22", "23", "24", "24", "26", "27", "21", "29", "30", "31", "32", "33", "34", "35", "24", "37", "38", "39", "40", "41", "42", "43", "33", "40", "46", "47", "45", "48", "48", "51", "39", "53", "54", "55", "56", "57", "58", "59", "45", "61", "62", "56", "63", "65", "66", "67", "51" ]
[ "nonn", "easy", "mult" ]
12
1
2
[ "A013662", "A047994", "A268335", "A350388", "A350389", "A384041", "A384046", "A384047", "A384048", "A384049", "A384050", "A384051", "A384052", "A384053", "A384054", "A384055", "A384056", "A384057", "A384058" ]
null
Amiram Eldar, May 18 2025
2025-05-21T23:19:01
oeisdata/seq/A384/A384054.seq
933972a8f591c820b48dacccba923cdc
A384055
The number of integers k from 1 to n such that the greatest divisor of k that is a unitary divisor of n is odd.
[ "1", "1", "3", "3", "5", "3", "7", "7", "9", "5", "11", "9", "13", "7", "15", "15", "17", "9", "19", "15", "21", "11", "23", "21", "25", "13", "27", "21", "29", "15", "31", "31", "33", "17", "35", "27", "37", "19", "39", "35", "41", "21", "43", "33", "45", "23", "47", "45", "49", "25", "51", "39", "53", "27", "55", "49", "57", "29", "59", "45", "61", "31", "63", "63", "65", "33", "67", "51", "69" ]
[ "nonn", "easy", "mult" ]
8
1
3
[ "A000265", "A006519", "A026741", "A047994", "A384046", "A384047", "A384048", "A384049", "A384050", "A384051", "A384052", "A384053", "A384054", "A384055", "A384056", "A384057", "A384058" ]
null
Amiram Eldar, May 18 2025
2025-05-21T01:33:18
oeisdata/seq/A384/A384055.seq
01d948ab9728a925883aa2625ce32435
A384056
The number of integers k from 1 to n such that the greatest divisor of k that is a unitary divisor of n is a power of 2.
[ "1", "2", "2", "4", "4", "4", "6", "8", "8", "8", "10", "8", "12", "12", "8", "16", "16", "16", "18", "16", "12", "20", "22", "16", "24", "24", "26", "24", "28", "16", "30", "32", "20", "32", "24", "32", "36", "36", "24", "32", "40", "24", "42", "40", "32", "44", "46", "32", "48", "48", "32", "48", "52", "52", "40", "48", "36", "56", "58", "32", "60", "60", "48", "64", "48", "40", "66", "64", "44" ]
[ "nonn", "easy", "mult" ]
8
1
2
[ "A000079", "A000265", "A006519", "A047994", "A062570", "A065463", "A384046", "A384047", "A384048", "A384049", "A384050", "A384051", "A384052", "A384053", "A384054", "A384055", "A384056", "A384057", "A384058" ]
null
Amiram Eldar, May 18 2025
2025-05-21T01:33:07
oeisdata/seq/A384/A384056.seq
fd715a34b94a90a4c4156db0dd2b96c4
A384057
The number of integers k from 1 to n such that the greatest divisor of k that is a unitary divisor of n is a 3-smooth number.
[ "1", "2", "3", "4", "4", "6", "6", "8", "9", "8", "10", "12", "12", "12", "12", "16", "16", "18", "18", "16", "18", "20", "22", "24", "24", "24", "27", "24", "28", "24", "30", "32", "30", "32", "24", "36", "36", "36", "36", "32", "40", "36", "42", "40", "36", "44", "46", "48", "48", "48", "48", "48", "52", "54", "40", "48", "54", "56", "58", "48", "60", "60", "54", "64", "48", "60", "66", "64" ]
[ "nonn", "easy", "mult" ]
11
1
2
[ "A003586", "A047994", "A065330", "A065331", "A065463", "A372671", "A384046", "A384047", "A384048", "A384049", "A384050", "A384051", "A384052", "A384053", "A384054", "A384055", "A384056", "A384057", "A384058" ]
null
Amiram Eldar, May 18 2025
2025-05-21T01:32:56
oeisdata/seq/A384/A384057.seq
a4e8b0c60061d92df0455417675d081d
A384058
The number of integers k from 1 to n such that the greatest divisor of k that is a unitary divisor of n is a 5-rough number (A007310).
[ "1", "1", "2", "3", "5", "2", "7", "7", "8", "5", "11", "6", "13", "7", "10", "15", "17", "8", "19", "15", "14", "11", "23", "14", "25", "13", "26", "21", "29", "10", "31", "31", "22", "17", "35", "24", "37", "19", "26", "35", "41", "14", "43", "33", "40", "23", "47", "30", "49", "25", "34", "39", "53", "26", "55", "49", "38", "29", "59", "30", "61", "31", "56", "63", "65", "22", "67", "51", "46" ]
[ "nonn", "easy", "mult" ]
10
1
3
[ "A007310", "A047994", "A065330", "A065331", "A384042", "A384046", "A384047", "A384048", "A384049", "A384050", "A384051", "A384052", "A384053", "A384054", "A384055", "A384056", "A384057", "A384058" ]
null
Amiram Eldar, May 18 2025
2025-05-21T01:33:02
oeisdata/seq/A384/A384058.seq
22afacfa256729d2697460ddf6b0438a
A384059
Decimal expansion of the circumradius of a regular pentagonal prism of edge length 1.
[ "9", "8", "6", "7", "1", "5", "1", "5", "5", "3", "2", "5", "9", "8", "3", "1", "0", "7", "3", "2", "0", "7", "0", "0", "0", "5", "5", "8", "4", "0", "6", "6", "8", "9", "1", "7", "8", "7", "2", "8", "5", "0", "4", "5", "2", "2", "3", "2", "0", "3", "5", "0", "7", "3", "7", "8", "6", "4", "3", "1", "5", "5", "2", "4", "8", "6", "1", "9", "6", "1", "0", "4", "0", "5", "4", "5", "3", "8", "1", "0", "3", "3", "0", "5", "7", "9", "1" ]
[ "nonn", "cons" ]
12
0
1
[ "A102771", "A300074", "A384036", "A384059" ]
null
Kritsada Moomuang, May 18 2025
2025-05-22T19:08:23
oeisdata/seq/A384/A384059.seq
ff90190fcb1619593e905848eb41988f