A392424 - OEIS

%I #6 Jan 13 2026 14:42:10

%S 144,324,400,576,784,1600,1728,1936,2304,2500,2704,2916,3136,3600,

%T 4624,5776,5832,6400,7056,7744,8000,8100,8464,9216,9604,10816,12544,

%U 13456,13824,14400,15376,15876,17424,18496,19600,20736,21904,21952,22500,23104,24336,25600

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

%C Intersection of A005843 and A386762.

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

%H Michael De Vlieger, <a href="/A392424/b392424.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Pow#powerful">Index entries for sequences related to powerful numbers</a>.

%e Table of n, a(n) for select n:

%e  n    a(n)

%e -----------------------------------

%e  1    144 = 12^2 = 2^4 *  3^2

%e  2    324 = 18^2 = 2^2 *  3^4

%e  3    400 = 20^2 = 2^4 *  5^2

%e  4    576 = 24^2 = 2^6 *  3^2

%e  5    784 = 28^2 = 2^4 *  7^2

%e  6   1600 = 40^2 = 2^6 *  5^2

%e  7   1728 = 12^3 = 2^6 *  3^3

%e  8   1936 = 44^2 = 2^4 * 11^2

%e  9   2304 = 48^2 = 2^8 *  3^2

%e 10   2500 = 50^2 = 2^2 *  5^4

%e 11   2704 = 52^2 = 2^4 * 13^2

%e 14   3600 = 60^2 = 2^4 *  3^2 * 5^2

%t 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]]

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

%K nonn,easy

%O 1,1

%A _Michael De Vlieger_, Jan 11 2026