A329445 Dirichlet inverse of A328745.

1, -2, -3, 1, -5, 6, -7, 0, 3, 10, -11, -3, -13, 14, 15, 0, -17, -6, -19, -5, 21, 22, -23, 0, 10, 26, -1, -7, -29, -30, -31, 0, 33, 34, 35, 3, -37, 38, 39, 0, -41, -42, -43, -11, -15, 46, -47, 0, 21, -20, 51, -13, -53, 2, 55, 0, 57, 58, -59, 15, -61, 62, -21, 0, 65, -66, -67, -17

Offset: 1

Author

Werner Schulte, Nov 13 2019

Keywords

• sign
• mult

Comments

Signed version of A182938.

Crossrefs

Cf. A008836, A182938, A328745.

Programs

Python

from math import prod, comb
from sympy import factorint
def A329445(n): return prod(-comb(p,e) if e&1 else comb(p,e) for p,e in factorint(n).items()) # Chai Wah Wu, Dec 23 2022

Formula

Multiplicative with a(p^e) = (-1)^e*binomial(p,e) for prime p and e >= 0.

Dirichlet g.f.: Sum_{n>0} a(n)/n^s = Product_{p prime} (1-p^(-s))^p.

a(n) = A182938(n) * A008836(n) for n > 0.