A323885 Sum of A001511 and its Dirichlet inverse.

2, 0, 0, 4, 0, 4, 0, 4, 1, 4, 0, 2, 0, 4, 2, 5, 0, 2, 0, 2, 2, 4, 0, 4, 1, 4, 1, 2, 0, 0, 0, 6, 2, 4, 2, 3, 0, 4, 2, 4, 0, 0, 0, 2, 1, 4, 0, 5, 1, 2, 2, 2, 0, 2, 2, 4, 2, 4, 0, 4, 0, 4, 1, 7, 2, 0, 0, 2, 2, 0, 0, 4, 0, 4, 1, 2, 2, 0, 0, 5, 1, 4, 0, 4, 2, 4, 2, 4, 0, 2, 2, 2, 2, 4, 2, 6, 0, 2, 1, 3, 0, 0, 0, 4, 0

Offset: 1

Author

Antti Karttunen, Feb 08 2019

Keywords

• nonn

Links

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

Crossrefs

Cf. A001511, A092673.

Cf. also A318449, A318450, A323365, A323882, A323884, A323887, A323896.

Programs

PARI

A001511(n) = (1+valuation(n,2));
A092673(n) = (moebius(n)-if(n%2,0,moebius(n/2)));
A323885(n) = (A001511(n)+A092673(n));

Python

from sympy import mobius
def A323885(n): return (n&-n).bit_length()+mobius(n)-(0 if n&1 else mobius(n>>1)) # Chai Wah Wu, Jul 13 2022

Formula

a(n) = A001511(n) + A092673(n).