A392424 Powers k^m, m > 1, of even k that are neither squarefree nor squareful.

144, 324, 400, 576, 784, 1600, 1728, 1936, 2304, 2500, 2704, 2916, 3136, 3600, 4624, 5776, 5832, 6400, 7056, 7744, 8000, 8100, 8464, 9216, 9604, 10816, 12544, 13456, 13824, 14400, 15376, 15876, 17424, 18496, 19600, 20736, 21904, 21952, 22500, 23104, 24336, 25600

Offset

1,1

Comments

Intersection of A005843 and A386762.

Powers k^m, m > 1, of k in A391026.

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   1728 = 12^3 = 2^6 *  3^3
 8   1936 = 44^2 = 2^4 * 11^2
 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 = 30000; i = 1; MapIndexed[Set[S[First[#2]], #1] &, Select[Range[2, Sqrt[nn], 2], 1 == Min[#] < Max[#] &@ FactorInteger[#][[All, -1]] &] ]; Union@ Reap[While[j = 2; While[S[i]^j < nn, Sow[S[i]^j]; j++]; j > 2, i++] ][[-1, 1]]

Crossrefs

Cf. A001597, A001694, A005843, A013929, A024619, A126706, A131605, A286708, A332785, A386762, A391026, A392423.

Sequence in context: A389864 A386762 A390379 * A389947 A392069 A217584

Adjacent sequences: A392421 A392422 A392423 * A392425 A392426 A392427

Keyword

nonn,easy

Author

Michael De Vlieger, Jan 11 2026

Status

approved