A378645 Dirichlet convolution of A055615 and A103977.

1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, -1, -1, -1, -1, -1, 3, -1, 1, -1, -1, -1, 3, -1, -1, -1, -1, -1, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, 5, -1, 11, -1, -1, -1, -1, -1, 3, -1, -1, -1, -1, -1, -1, -1, 7, -1, -1, -1, -3, -1, -1, -1, -1, -1, 11, -1, -1, -1, 3, -1, -1, -1, -1, -1, -1, -1, 11, -1, 5, -1, -1, -1, 3

Offset: 1

Author

Antti Karttunen, Dec 03 2024

Keywords

• sign

Links

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

Crossrefs

Cf. A055615, A263837, A103977, A153881, A378646 (Dirichlet inverse).

Programs

PARI

A055615(n) = (n*moebius(n));
A378645(n) = sumdiv(n,d,A055615(d)*A103977(n/d));

Formula

a(n) = Sum_{d|n} A055615(d)*A103977(n/d).

a(n) = A153881(n) always when n is a non-abundant number (A263837), and also for some of the abundant numbers, A005101.