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A175496 Positive integers k where k is not squarefree but the number of divisors of k is a power of 2.

%I A175496 #26 Jan 05 2023 03:14:22
%S A175496 8,24,27,40,54,56,88,104,120,125,128,135,136,152,168,184,189,216,232,
%T A175496 248,250,264,270,280,296,297,312,328,343,344,351,375,376,378,384,408,
%U A175496 424,440,456,459,472,488,513,520,536,552,568,584,594,616,621,632,640
%N A175496 Positive integers k where k is not squarefree but the number of divisors of k is a power of 2.
%C A175496 This sequence is not the same as sequence A048109.
%C A175496 The asymptotic density of this sequence is A327839 - A059956 = 0.0799000375... - _Amiram Eldar_, Nov 01 2020
%H A175496 Amiram Eldar, <a href="/A175496/b175496.txt">Table of n, a(n) for n = 1..10000</a>
%t A175496 pow2Q[n_] := n == 2^IntegerExponent[n, 2]; aQ[n_] := ! SquareFreeQ[n] && pow2Q[DivisorSigma[0, n]]; Select[Range[640], aQ] (* _Amiram Eldar_, Sep 21 2019 *)
%o A175496 (PARI) isok(k) = my(d=numdiv(k)); !issquarefree(k) && (2^valuation(d, 2) == d); \\ _Michel Marcus_, Nov 20 2020
%o A175496 (Python)
%o A175496 from itertools import count, islice
%o A175496 from sympy import factorint
%o A175496 def A175496_gen(startvalue=2): # generator of terms >= startvalue
%o A175496     return filter(lambda n:max(f:=factorint(n).values())>1 and all(map(lambda m:not((k:=m+1)&-k)^k,f)),count(max(startvalue,2)))
%o A175496 A175496_list = list(islice(A175496_gen(),30)) # _Chai Wah Wu_, Jan 04 2023
%Y A175496 Cf. A059956, A327839.
%Y A175496 Complement of A005117 within A036537.
%Y A175496 Subsequence of A013929.
%Y A175496 A048109, A062838\{1}, A113852 are subsequences.
%K A175496 nonn
%O A175496 1,1
%A A175496 _Leroy Quet_, May 30 2010
%E A175496 Extended by _D. S. McNeil_, May 31 2010