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%I #10 Nov 21 2021 10:18:16
%S 1,0,0,1,1,0,2,0,1,0,3,0,4,0,0,1,5,0,6,1,0,0,7,0,8,0,0,2,9,0,10,0,0,0,
%T 8,1,12,0,0,0,13,0,14,3,1,0,15,0,15,0,0,4,17,0,14,0,0,0,19,0,20,0,2,1,
%U 16,0,22,5,0,0,23,0,24,0,0,6,20,0,26,1,1,0,27,0,22,0,0,0,29,0,24,7,0,0,24,0,32,0
%N Dirichlet convolution of A126760 with Liouville's lambda.
%H Antti Karttunen, <a href="/A349395/b349395.txt">Table of n, a(n) for n = 1..20000</a>
%t f[n_] := 2 * Floor[(m = n/2^IntegerExponent[n, 2]/3^IntegerExponent[n, 3])/6] + Mod[m, 3]; a[n_] := DivisorSum[n, f[#] * LiouvilleLambda[n/#] &]; Array[a, 100] (* _Amiram Eldar_, Nov 16 2021 *)
%o (PARI)
%o A008836(n) = ((-1)^bigomega(n));
%o A126760(n) = {n&&n\=3^valuation(n, 3)<<valuation(n, 2); n%3+n\6*2}; \\ From A126760
%o A349395(n) = sumdiv(n,d,A126760(n/d)*A008836(d));
%Y Cf. A008836, A126760.
%Y Cf. A347233, A347234, A349390, A349391, A349392, A349393 for other Dirichlet convolutions of A126760. And also A349375.
%K nonn
%O 1,7
%A _Antti Karttunen_, Nov 15 2021