A378213 Dirichlet inverse of A140773.

1, -2, -2, 0, -2, 3, -2, 2, 0, 3, -2, 2, -2, 3, 3, -1, -2, 2, -2, 2, 3, 3, -2, -4, 0, 3, 2, 2, -2, -2, -2, 0, 3, 3, 3, -3, -2, 3, 3, -4, -2, -2, -2, 2, 2, 3, -2, 0, 0, 2, 3, 2, -2, -4, 3, -4, 3, 3, -2, -6, -2, 3, 2, 0, 3, -2, -2, 2, 3, -2, -2, -2, -2, 3, 2, 2, 3, -2, -2, 0, -1, 3, -2, -6, 3, 3, 3, -4, -2, -6, 3, 2, 3, 3, 3, 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, A378214, A378215 (parity of terms).

Programs

PARI

A065043(n) = (1 - (bigomega(n)%2));
A038548(n) = sumdiv(n,d,A065043(d));
A140773(n) = sumdiv(n,d,A038548(d));
memoA378213 = Map();
A378213(n) = if(1==n,1,my(v); if(mapisdefined(memoA378213,n,&v), v, v = -sumdiv(n,d,if(dA140773(n/d)*A378213(d),0)); mapput(memoA378213,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA140773(n/d) * a(d).