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A295661 Numbers with at least one odd exponent larger than one in their prime factorization.

%I A295661 #18 May 19 2022 09:20:31
%S A295661 8,24,27,32,40,54,56,72,88,96,104,108,120,125,128,135,136,152,160,168,
%T A295661 184,189,200,216,224,232,243,248,250,264,270,280,288,296,297,312,328,
%U A295661 343,344,351,352,360,375,376,378,384,392,408,416,424,432,440,456,459,472,480,486,488,500,504,512,513,520,536,540
%N A295661 Numbers with at least one odd exponent larger than one in their prime factorization.
%C A295661 The asymptotic density of this sequence is 1 - Product_{p prime} (1 - 1/(p^2*(p+1))) = 0.1184861602... (= 1 - A065465). - _Amiram Eldar_, May 18 2022
%H A295661 Antti Karttunen, <a href="/A295661/b295661.txt">Table of n, a(n) for n = 1..10000</a>
%t A295661 Select[Range[540], Count[FactorInteger[#][[All, -1]], _?(And[OddQ@ #, # > 1] &)] > 0 &] (* _Michael De Vlieger_, Nov 28 2017 *)
%o A295661 (Python)
%o A295661 from sympy import factorint
%o A295661 def ok(n):
%o A295661     return max((e for e in factorint(n).values() if e%2), default=-1) > 1
%o A295661 print(list(filter(ok, range(541)))) # _Michael S. Branicky_, Aug 24 2021
%Y A295661 Positions of nonzero terms in A295662 and A295663.
%Y A295661 Subsequence of A046099 (64 = 2^6, although a cube, is not in this sequence).
%Y A295661 Differs from A060476 (256 = 2^8 is not a member of this sequence).
%Y A295661 Complement of A335275.
%Y A295661 Cf. A065465.
%K A295661 nonn
%O A295661 1,1
%A A295661 _Antti Karttunen_, Nov 28 2017