A358679 Dirichlet inverse of the characteristic function of A061345, odd prime powers.

1, 0, -1, 0, -1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 2, 0, -1, 0, -1, 0, 2, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 2, 0, 2, 0, -1, 0, 2, 0, -1, 0, -1, 0, -1, 0, -1, 0, 0, 0, 2, 0, -1, 0, 2, 0, 2, 0, -1, 0, -1, 0, -1, 0, 2, 0, -1, 0, 2, 0, -1, 0, -1, 0, -1, 0, 2, 0, -1, 0, 0, 0, -1, 0, 2, 0, 2, 0, -1, 0, 2, 0, 2, 0, 2, 0, -1, 0, -1, 0, -1, 0, -1, 0, -6

Offset: 1

Author

Antti Karttunen, Dec 23 2022

Keywords

• sign

Links

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

Crossrefs

Cf. A061345, A174275.

Programs

PARI

A174275(n) = ((n%2)&&isprimepower(n));
memoA358679 = Map();
A358679(n) = if(1==n,1,my(v); if(mapisdefined(memoA358679,n,&v), v, v = -sumdiv(n,d,if(dA174275(n/d)*A358679(d),0)); mapput(memoA358679,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA174275(n/d) * a(d).