A369909 a(n) = n * Sum_{p|n, p prime} Omega(n/p) / p.

0, 0, 0, 2, 0, 5, 0, 8, 3, 7, 0, 20, 0, 9, 8, 24, 0, 30, 0, 28, 10, 13, 0, 60, 5, 15, 18, 36, 0, 62, 0, 64, 14, 19, 12, 90, 0, 21, 16, 84, 0, 82, 0, 52, 48, 25, 0, 160, 7, 70, 20, 60, 0, 135, 16, 108, 22, 31, 0, 186, 0, 33, 60, 160, 18, 122, 0, 76, 26, 118, 0, 240, 0

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. A001222 (Omega), A369741, A369908.

Cf. also A369894.

Programs

Mathematica

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

PARI

A369909(n) = if(1==n, 0, my(f=factor(n)); n*sum(i=1, #f~, (bigomega(n/f[i, 1])/f[i,1]))); \\ Antti Karttunen, Jan 22 2025

Formula

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