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

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, 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, 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

Offset: 1

Author

Antti Karttunen, Jan 16 2023

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000

Crossrefs

Cf. A320655, A322353 (seems to give the absolute values), A359786.

Programs

PARI

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));
memoA359785 = Map();
A359785(n) = if(1==n,1,my(v); if(mapisdefined(memoA359785,n,&v), v, v = -sumdiv(n,d,if(dA320655(n/d)*A359785(d),0)); mapput(memoA359785,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA320655(n/d) * a(d).