A359815 Dirichlet inverse of A359770, where A359770(n) = 1 if n and bigomega(n) are of different parity, otherwise 0.

1, -1, 0, 1, 0, 0, 0, -2, -1, 0, 0, -1, 0, 0, -1, 3, 0, 1, 0, -1, -1, 0, 0, 2, -1, 0, 0, -1, 0, 1, 0, -5, -1, 0, -1, -1, 0, 0, -1, 2, 0, 1, 0, -1, 0, 0, 0, -4, -1, 1, -1, -1, 0, 0, -1, 2, -1, 0, 0, -1, 0, 0, 0, 8, -1, 1, 0, -1, -1, 1, 0, 2, 0, 0, 0, -1, -1, 1, 0, -4, 0, 0, 0, -1, -1, 0, -1, 2, 0, 0, -1, -1, -1, 0, -1, 8

Offset: 1

Author

Antti Karttunen, Jan 15 2023

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A001222, A069345, A353556, A353557, A359770, A359816 (parity of terms), A359817 (positions of odd terms).

Cf. also A358777 (Dirichlet inverse of A353557), A359763 [= a(A003961(n))], A359814.

Programs

PARI

A359770(n) = ((n-bigomega(n))%2);
memoA359815 = Map();
A359815(n) = if(1==n,1,my(v); if(mapisdefined(memoA359815,n,&v), v, v = -sumdiv(n,d,if(dA359770(n/d)*A359815(d),0)); mapput(memoA359815,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA359770(n/d) * a(d).