A390381 Powers k^m, m > 3, with k neither squarefree nor squareful.

20736, 104976, 160000, 248832, 331776, 614656, 1889568, 2560000, 2985984, 3200000, 3748096, 4100625, 5308416, 6250000, 7311616, 7962624, 8503056, 9834496, 12960000, 15752961, 17210368, 21381376, 31640625, 33362176, 34012224, 35831808, 40960000, 49787136, 59969536

Offset

1,1

Comments

Intersection of A036967 and A386762 = intersection of A036967 and A388549.

A388549 is the union of this sequence and A392564.

A386762 is the union of this sequence, A389947, and A392564.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Index entries for sequences related to powerful numbers.

Example

Table of n, a(n) for select n:
 n        a(n)
---------------------------------------
 1      20736 = 12^4 = 2^8  * 3^4
 2     104976 = 18^4 = 2^4  * 3^8
 3     160000 = 20^4 = 2^8  * 5^4
 4     248832 = 12^5 = 2^10 * 3^5
 5     331776 = 24^4 = 2^12 * 3^4
 6     614656 = 28^4 = 2^8  * 7^4
 7    1889568 = 18^5 = 2^5  * 3^10
 8    2560000 = 40^4 = 2^12 * 5^4
 9    2985984 = 12^6 = 2^12 * 3^6
10    3200000 = 20^5 = 2^10 * 5^5
12    4100625 = 45^4 = 3^8  * 5^4
19   12960000 = 60^4 = 2^8  * 3^4 * 5^4

Mathematica

nn = 60000000; i = 1; MapIndexed[Set[S[First[#2]], #1] &, Select[Range@ Surd[nn, 4], 1 == Min[#] < Max[#] &@ FactorInteger[#][[All, -1]] &]]; Union@ Reap[While[j = 4; While[S[i]^j < nn, Sow[S[i]^j]; j++]; j > 4, i++] ][[-1, 1]]

Crossrefs

Cf. A390379, A392564.

Supersets: A001597, A001694, A013929, A024619, A036967, A126706, A131605, A286708, A386762, A388549.

Sequence in context: A183631 A340175 A176771 * A223237 A017404 A017524

Adjacent sequences: A390378 A390379 A390380 * A390382 A390383 A390384

Keyword

nonn,easy

Author

Michael De Vlieger, Jan 30 2026

Status

approved