A369907 a(n) = n * Sum_{p|n, p prime} omega(n/p) / p.

0, 0, 0, 2, 0, 5, 0, 4, 3, 7, 0, 16, 0, 9, 8, 8, 0, 21, 0, 24, 10, 13, 0, 32, 5, 15, 9, 32, 0, 62, 0, 16, 14, 19, 12, 60, 0, 21, 16, 48, 0, 82, 0, 48, 39, 25, 0, 64, 7, 45, 20, 56, 0, 63, 16, 64, 22, 31, 0, 154, 0, 33, 51, 32, 18, 122, 0, 72, 26, 118, 0, 120, 0, 39

Offset: 1

Author

Wesley Ivan Hurt, Feb 05 2024

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A001221 (omega), A345354, A345355, A369744.

Cf. also A369894, A369909, A369779.

Programs

Mathematica

Table[n*DivisorSum[n, PrimeNu[n/#]/# &, PrimeQ[#] &], {n, 100}]

PARI

A369907(n) = if(1==n, 0, my(f=factor(n)); n*sum(i=1, #f~, (omega(n/f[i, 1])/f[i,1]))); \\ Antti Karttunen, Jan 23 2025

Formula

a(p^k) = p^(k-1), for p prime and k >= 1. - Wesley Ivan Hurt, Jun 26 2024