The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #9 Dec 23 2025 16:25:10
%S 24,40,48,54,56,80,88,96,104,112,120,135,136,152,160,162,168,176,184,
%T 189,192,208,224,232,240,248,250,264,270,272,280,296,297,304,312,320,
%U 328,336,344,351,352,360,368,375,376,378,384,405,408,416,424,440,448,456
%N Numbers that are neither cubefree nor powerful.
%C Intersection of A046099 and A332785.
%C A332785 is the union of this sequence and A386684, disjoint subsets.
%C A378767 is the union of this sequence and A372404, disjoint subsets.
%H Michael De Vlieger, <a href="/A391319/b391319.txt">Table of n, a(n) for n = 1..10000</a>
%e Table of n, a(n) for select n:
%e n a(n)
%e ---------------------------
%e 1 24 = 2^3 * 3
%e 2 40 = 2^3 * 5
%e 3 48 = 2^4 * 3
%e 4 54 = 2 * 3^3
%e 5 56 = 2^3 * 7
%e 6 80 = 2^4 * 5
%e 7 88 = 2^3 * 11
%e 11 120 = 2^3 * 3 * 5
%e 12 135 = 3^3 * 5
%e 17 168 = 2^3 * 3 * 7
%e 76 600 = 2^3 * 3 * 5^2
%e 111 840 = 2^3 * 3 * 5 * 7
%t fQ[x_] := And[MemberQ[#, 1], AnyTrue[#, # > 2 &]] &[FactorInteger[x][[;; , -1]] ]; Select[Range[500], fQ]
%Y Cf. A013929, A024619, A046099, A052485, A126706, A332785, A372404, A378767, A386684.
%K nonn
%O 1,1
%A _Michael De Vlieger_, Dec 07 2025