A378655 Dirichlet convolution of A153881 with the Dirichlet inverse of A103977.

1, -2, -3, 0, -5, 6, -7, 0, 0, 10, -11, -4, -13, 14, 15, 0, -17, -4, -19, -2, 21, 22, -23, 0, 0, 26, 0, 0, -29, -42, -31, 0, 33, 34, 35, 12, -37, 38, 39, -4, -41, -54, -43, 0, 0, 46, -47, 0, 0, 0, 51, 0, -53, 8, 55, -8, 57, 58, -59, 34, -61, 62, 0, 0, 65, -78, -67, 0, 69, -74, -71, -8, -73, 74, 0, 0, 77, -90, -79, 0, 0

Offset: 1

Author

Antti Karttunen, Dec 04 2024

Keywords

• sign

Links

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

Crossrefs

Cf. A055615, A103977, A153881, A263837, A378643, A378647 (Dirichlet inverse).

Programs

PARI

A153881(n) = if(n>1, -1, 1);
A378655(n) = sumdiv(n,d,A153881(d)*A378643(n/d));

Formula

a(n) = Sum_{d|n} A153881(d)*A378643(n/d).

a(n) = A055615(n) when n is a non-abundant number (A263837), and also for some subset of the abundant numbers, A005101.