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%I #11 Dec 24 2022 03:37:17
%S 1,1,-1,-1,-1,-1,1,-1,-1,-1,1,1,-1,1,1,-1,1,-1,1,1,-1,1,-1,1,-1,-1,-1,
%T -1,1,1,1,1,-1,1,-1,1,-1,1,1,1,1,-1,1,-1,1,-1,1,1,1,-1,-1,1,-1,-1,-1,
%U -1,-1,1,-1,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,1,1,-1,-1,1,-1,1,1,1,1,1,1,-1,1,-1,1,-1,-1,-1,1,-1,1,-1,1,-1,-1,1,1,-1,1,1,-1,-1,1,1
%N a(n) = lambda(n) * lambda(sigma(n)), where lambda is Liouville's lambda, and sigma is the sum of divisors function.
%H Antti Karttunen, <a href="/A359166/b359166.txt">Table of n, a(n) for n = 1..100000</a>
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F Multiplicative with a(p^e) = (-1)^(e + A001222(1 + p + p^2 + ... + p^e)).
%F a(n) = A008836(n) * A358766(n) = A008836(n) * A008836(A000203(n)).
%o (PARI) A359166(n) = ((-1)^(bigomega(n)+bigomega(sigma(n))));
%o (Python)
%o from functools import reduce
%o from operator import ixor
%o from collections import Counter
%o from sympy import factorint
%o def A359166(n): return (-1 if reduce(ixor, (f:=factorint(n)).values(),0)&1 else 1)*(-1 if reduce(ixor, sum((Counter(factorint((p**(e+1)-1)//(p-1))) for p, e in f.items()),Counter()).values(),0)&1 else 1) # _Chai Wah Wu_, Dec 23 2022
%Y Cf. A000203, A001222, A008836, A058063, A358766, A359167 (positions of positive terms), A359168 (of negative terms).
%K sign,mult
%O 1
%A _Antti Karttunen_, Dec 19 2022
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