cp's OEIS Frontend

A378767 Numbers k that are not prime powers which are divisible by a cube greater than 1.

%I A378767 #5 Dec 08 2024 17:28:17
%S A378767 24,40,48,54,56,72,80,88,96,104,108,112,120,135,136,144,152,160,162,
%T A378767 168,176,184,189,192,200,208,216,224,232,240,248,250,264,270,272,280,
%U A378767 288,296,297,304,312,320,324,328,336,344,351,352,360,368,375,376,378,384
%N A378767 Numbers k that are not prime powers which are divisible by a cube greater than 1.
%C A378767 Products m = j*k such that omega(k) = omega(m) > omega(j), where rad(j) | k but j does not divide k, with rad = A007947 and omega = A001221.
%C A378767 Proper subset of A126706.
%C A378767 This sequence is distinct from A362148, since this sequence also contains 216, 432, etc.
%H A378767 Michael De Vlieger, <a href="/A378767/b378767.txt">Table of n, a(n) for n = 1..10000</a>
%F A378767 {a(n)} = { k : omega(k) > 1, there exists p | k such that p^3 | k }.
%F A378767 Intersection of A046099 and A024619.
%F A378767 Union of A362148 and A372695.
%e A378767 Prime decomposition of select a(n) = m, showing m = j*k:
%e A378767 a(1) = 24 = 2^3 * 3 = 4 * 6.
%e A378767 a(2) = 40 = 2^3 * 5 = 4 * 10.
%e A378767 a(3) = 48 = 2^4 * 3 = 8 * 6.
%e A378767 a(4) = 54 = 2 * 3^3 = 9 * 6.
%e A378767 a(5) = 56 = 2^3 * 7 = 4 * 14.
%e A378767 a(6) = 72 = 2^3 * 3^2 = 4 * 18.
%e A378767 a(9) = 96 = 2^5 * 3 = 8 * 12 = 16 * 6.
%e A378767 a(130) = 864 = 2^5 * 3^2 = 8 * 108 = 9 * 96 = 16 * 54, etc.
%t A378767 Select[Select[Range[2^10], AnyTrue[FactorInteger[#][[All, -1]], # > 2 &] &], Not@*PrimePowerQ]
%Y A378767 Cf. A024619, A046099, A126706, A362148, A372695.
%K A378767 nonn,easy
%O A378767 1,1
%A A378767 _Michael De Vlieger_, Dec 06 2024