A369455 Dirichlet convolution of A083345 with A055615 (Dirichlet inverse of n), where A083345(n) = (n'/gcd(n,n')) and n' is the arithmetic derivative of n.

0, 1, 1, -1, 1, 0, 1, 1, -1, 0, 1, -3, 1, 0, 0, -4, 1, -6, 1, -3, 0, 0, 1, 0, -3, 0, -5, -3, 1, 0, 1, 1, 0, 0, 0, 9, 1, 0, 0, 0, 1, 0, 1, -3, -6, 0, 1, -3, -5, -20, 0, -3, 1, -8, 0, 0, 0, 0, 1, 0, 1, 0, -6, -7, 0, 0, 1, -3, 0, 0, 1, -6, 1, 0, -20, -3, 0, 0, 1, -3, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, -3, 0, 0, 0, 0, 1, -42, -6, 29

Offset: 1

Author

Antti Karttunen, Jan 27 2024

Keywords

• sign

Comments

Dirichlet convolution of this sequence with A000010 (Euler phi) is A369068.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A055615, A083345.

Cf. also A349394, A349396, A369068, A369069.

Programs

PARI

A055615(n) = (n*moebius(n));
A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
A369455(n) = sumdiv(n, d, A083345(n/d)*A055615(d));

Formula

a(n) = Sum_{d|n} A055615(n/d)*A083345(d).