A359814 Dirichlet inverse of A359769, where A359769(n) = A353557(n) - A353556(n).

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..16384

Crossrefs

Cf. A001222, A353556, A353557, A359769, A359816 (parity of terms).

Cf. also A358777 (Dirichlet inverse of A353557), A359763 [= a(A003961(n))], A359815.

Programs

PARI

A353556(n) = ((!(n%2))&&(bigomega(n)%2));
A353557(n) = ((n%2)&&(!(bigomega(n)%2)));
A359769(n) = (A353557(n)-A353556(n));
memoA359814 = Map();
A359814(n) = if(1==n,1,my(v); if(mapisdefined(memoA359814,n,&v), v, v = -sumdiv(n,d,if(dA359769(n/d)*A359814(d),0)); mapput(memoA359814,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA359769(n/d) * a(d).