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A359785 Dirichlet inverse of A320655, where A320655(n) is the number of factorizations of n into semiprimes.

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%I A359785 #9 Oct 05 2023 16:25:15
%S A359785 1,0,0,-1,0,-1,0,0,-1,-1,0,0,0,-1,-1,0,0,0,0,0,-1,-1,0,1,-1,-1,0,0,0,
%T A359785 0,0,0,-1,-1,-1,1,0,-1,-1,1,0,0,0,0,0,-1,0,0,-1,0,-1,0,0,1,-1,1,-1,-1,
%U A359785 0,2,0,-1,0,0,-1,0,0,0,-1,0,0,0,0,-1,0,0,-1,0,0,0,0,-1,0,2,-1,-1,-1,1,0,2,-1,0,-1,-1,-1,0,0,0,0,1,0,0,0,1,0
%N A359785 Dirichlet inverse of A320655, where A320655(n) is the number of factorizations of n into semiprimes.
%H A359785 Antti Karttunen, <a href="/A359785/b359785.txt">Table of n, a(n) for n = 1..100000</a>
%F A359785 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A320655(n/d) * a(d).
%o A359785 (PARI)
%o A359785 A320655(n, m=n) = if(1==n, 1, my(s=0); fordiv(n, d, if((2==bigomega(d)&&(d<=m)), s += A320655(n/d, d))); (s));
%o A359785 memoA359785 = Map();
%o A359785 A359785(n) = if(1==n,1,my(v); if(mapisdefined(memoA359785,n,&v), v, v = -sumdiv(n,d,if(d<n,A320655(n/d)*A359785(d),0)); mapput(memoA359785,n,v); (v)));
%Y A359785 Cf. A320655, A322353 (seems to give the absolute values), A359786.
%K A359785 sign
%O A359785 1,60
%A A359785 _Antti Karttunen_, Jan 16 2023