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Numbers with at least one odd exponent larger than one in their prime factorization.
5

%I #18 May 19 2022 09:20:31

%S 8,24,27,32,40,54,56,72,88,96,104,108,120,125,128,135,136,152,160,168,

%T 184,189,200,216,224,232,243,248,250,264,270,280,288,296,297,312,328,

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

%C 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 Antti Karttunen, <a href="/A295661/b295661.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Range[540], Count[FactorInteger[#][[All, -1]], _?(And[OddQ@ #, # > 1] &)] > 0 &] (* _Michael De Vlieger_, Nov 28 2017 *)

%o (Python)

%o from sympy import factorint

%o def ok(n):

%o return max((e for e in factorint(n).values() if e%2), default=-1) > 1

%o print(list(filter(ok, range(541)))) # _Michael S. Branicky_, Aug 24 2021

%Y Positions of nonzero terms in A295662 and A295663.

%Y Subsequence of A046099 (64 = 2^6, although a cube, is not in this sequence).

%Y Differs from A060476 (256 = 2^8 is not a member of this sequence).

%Y Complement of A335275.

%Y Cf. A065465.

%K nonn

%O 1,1

%A _Antti Karttunen_, Nov 28 2017