A383286 Dirichlet convolution of A276086 (primorial base exp-function) with A055615 (Dirichlet inverse of n).

2, -1, 0, 3, 8, -4, -4, -3, 12, 14, 68, 6, 24, 62, 96, 195, 416, 86, 212, 270, 720, 956, 2204, 584, 1160, 1788, 3660, 5454, 11192, -300, -48, -429, -228, -820, 20, -260, -4, -376, 60, -420, 548, -1462, 264, -1758, 540, -2902, 3056, -960, 1680, 80, 3900, 4086, 15644, -3320, 8212, 1896, 25500, 16904, 78632, -850, -24, 150

Offset: 1

Author

Antti Karttunen, May 12 2025

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..30030
• Index entries for sequences related to primorial base.

Crossrefs

Cf. A055615, A276086.

Cf. also A349394, A369010.

Programs

PARI

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A055615(n) = (n*moebius(n));
A383286(n) = sumdiv(n,d,A276086(n/d)*A055615(d));

Formula

a(n) = Sum_{d|n} A276086(n/d)*A055615(d).