A392069 Powers k^m divisible by only 1 prime cube, with m > 1 and nonsquarefree weak k (in A332785).

144, 324, 400, 576, 784, 1600, 1936, 2025, 2304, 2500, 2704, 2916, 3136, 3600, 3969, 4624, 5625, 5776, 6400, 7056, 7744, 8100, 8464, 9216, 9604, 9801, 10816, 12544, 13456, 13689, 14400, 15376, 15876, 17424, 18225, 18496, 19600, 21609, 21904, 22500, 23104, 23409, 24336, 25600, 26244, 26896, 28224, 29241, 29584, 30625, 30976, 33856

Offset

1,1

Comments

Numbers of the form k^2 * p^m, with squarefree k > 1 (in A062503), prime p, and m > 2, such that k and p are coprime.

A389947 is a superset; A389947(52) = 32400 = 2^4 * 3^4 * 5^2 is not a term in this sequence.

This sequence is A386762 \ A391968.

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    144 = 12^2 = 2^4 *  3^2
 2    324 = 18^2 = 2^2 *  3^4
 3    400 = 20^2 = 2^4 *  5^2
 4    576 = 24^2 = 2^6 *  3^2
 5    784 = 28^2 = 2^4 *  7^2
 6   1600 = 40^2 = 2^6 *  5^2
 7   1936 = 44^2 = 2^4 * 11^2
 8   2025 = 45^2 = 3^4 *  5^2
 9   2304 = 48^2 = 2^8 *  3^2
10   2500 = 50^2 = 2^2 *  5^4
11   2704 = 52^2 = 2^4 * 13^2
14   3600 = 60^2 = 2^4 *  3^2 * 5^2

Mathematica

nn = 32400; i = 1; MapIndexed[Set[S[First[#2]], #1] &, Select[Range@ Sqrt[nn], 1 == Min[#] < Max[#] &@ FactorInteger[#][[All, -1]] &] ]; Union@ Reap[While[j = 2; While[S[i]^j < nn, If[Count[FactorInteger[#][[All, -1]], _?(# > 2 &)] < 2, Sow[#]] &[S[i]^j]; j++]; j > 2, i++] ][[-1, 1]]

Crossrefs

Cf. A062503, A332785.

Supersets: A001597, A001694, A013929, A024619, A126706, A131605, A286708, A359280, A386762, A389864, A389947, A391968.

Sequence in context: A390379 A392424 A389947 * A217584 A030633 A189988

Adjacent sequences: A392066 A392067 A392068 * A392070 A392071 A392072

Keyword

nonn,easy

Author

Michael De Vlieger, Jan 07 2026

Status

approved