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%I #31 Feb 05 2024 18:09:19
%S 1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,
%T 1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,1,0,0,0,
%U 1,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,1
%N a(n) = 1 if n is an odd number with an even number of prime factors (counted with multiplicity), otherwise 0.
%H Antti Karttunen, <a href="/A353557/b353557.txt">Table of n, a(n) for n = 1..65537</a>
%H Jon Maiga, <a href="http://sequencedb.net/s/A353557">Computer-generated formulas for A353557</a>, Sequence Machine.
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F a(n) = A000035(n) * A065043(n).
%F a(n) = A000035(n) - A353558(n).
%F a(n) = A065043(n) - A353555(n).
%F For n >= 1, A353480(n) <= a(n) <= A353374(n).
%F For n >= 1, a(n) = A059841(A327858(n)). [See comments in the latter sequence]
%F a(n) = [A166698(n) > 0], where [ ] is the Iverson bracket. - _Antti Karttunen_, Dec 30 2022
%F a(n) = A059841(A095112(n)). [From Sequence Machine] - _Antti Karttunen_, Nov 22 2023
%F a(n) = A353495(n) + A360109(n). - _Antti Karttunen_, Feb 05 2024
%o (PARI) A353557(n) = ((n%2)&&(!(bigomega(n)%2)));
%o (Python)
%o from functools import reduce
%o from operator import ixor
%o from sympy import factorint
%o def A353557(n): return 1&n&(reduce(ixor,factorint(n).values(),0)^1) # _Chai Wah Wu_, Dec 21 2022
%Y Characteristic function of A046337.
%Y Cf. A000035, A001222, A059841, A065043, A095112, A166698, A327858, A353374, A353480, A353555, A353556, A353558, A358777 (Dirichlet inverse), A369257 (inverse Möbius transform).
%Y Cf. also A353495, A360109, A369001.
%K nonn
%O 1
%A _Antti Karttunen_, May 01 2022
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