A039697 a(n) = Sum(p_j) * Sum(k_j) where n = Product(p_j^k_j).

0, 2, 3, 4, 5, 10, 7, 6, 6, 14, 11, 15, 13, 18, 16, 8, 17, 15, 19, 21, 20, 26, 23, 20, 10, 30, 9, 27, 29, 30, 31, 10, 28, 38, 24, 20, 37, 42, 32, 28, 41, 36, 43, 39, 24, 50, 47, 25, 14, 21, 40, 45, 53, 20, 32, 36, 44, 62, 59, 40, 61, 66, 30, 12, 36, 48, 67, 57, 52, 42, 71, 25

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• easy

Examples

			14 = 2^1 * 7^1, a(14) = (2+7)*(1+1) = 18.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Termwise product of A001222 and A008472.

Programs

Mathematica

Array[If[# == 1, 0, Plus@@First/@FactorInteger[ # ]*Plus@@Last/@FactorInteger[ # ]]&, 5! ] (* Vladimir Joseph Stephan Orlovsky, Feb 28 2010 *)

PARI

a(n) = if(n == 1, 0, my(f = factor(n)); vecsum(f[,1]) * vecsum(f[,2])); \\ Amiram Eldar, Jun 09 2025

Formula

a(n) = A001222(n) * A008472(n).

Extensions

a(1) corrected by Amiram Eldar, Jun 09 2025