A378214 Dirichlet inverse of A369255, where A369255(n) = A140773(n) mod 2.

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

Offset: 1

Author

Antti Karttunen, Nov 22 2024

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A140773, A369255, A378213, A378215 (parity of terms).

Cf. also conjectured formula in A252505.

Programs

PARI

A065043(n) = (1 - (bigomega(n)%2));
A038548(n) = sumdiv(n,d,A065043(d));
A140773(n) = sumdiv(n,d,A038548(d));
A369255(n) = (A140773(n)%2);
memoA378214 = Map();
A378214(n) = if(1==n,1,my(v); if(mapisdefined(memoA378214,n,&v), v, v = -sumdiv(n,d,if(dA369255(n/d)*A378214(d),0)); mapput(memoA378214,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA369255(n/d) * a(d).