A369454 Dirichlet inverse of A369257, where A369257 is the number of divisors of n that are odd numbers with an even number of prime factors with multiplicity.

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

Offset: 1

Author

Antti Karttunen, Jan 27 2024

Keywords

• sign

Links

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

Crossrefs

Cf. A353557, A369257.

Cf. also A358777, A369454.

Programs

PARI

A353557(n) = ((n%2)&&(!(bigomega(n)%2)));
A369257(n) = sumdiv(n,d,A353557(d));
memoA369454 = Map();
A369454(n) = if(1==n,1,my(v); if(mapisdefined(memoA369454,n,&v), v, v = -sumdiv(n,d,if(dA369257(n/d)*A369454(d),0)); mapput(memoA369454,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA369257(n/d) * a(d).