A369741 a(n) = Sum_{p|n, p prime} p^Omega(n/p).

0, 1, 1, 2, 1, 5, 1, 4, 3, 7, 1, 13, 1, 9, 8, 8, 1, 13, 1, 29, 10, 13, 1, 35, 5, 15, 9, 53, 1, 38, 1, 16, 14, 19, 12, 35, 1, 21, 16, 133, 1, 62, 1, 125, 34, 25, 1, 97, 7, 29, 20, 173, 1, 35, 16, 351, 22, 31, 1, 160, 1, 33, 58, 32, 18, 134, 1, 293, 26, 78, 1, 97, 1, 39

Offset: 1

Author

Wesley Ivan Hurt, Jan 30 2024

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A001222 (Omega), A307409, A369909.

Cf. also A345301.

Programs

Mathematica

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

PARI

A369741(n) = if(1==n, 0, my(f=factor(n)); sum(i=1, #f~, f[i,1]^bigomega(n/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