A064939 a(n) = Sum_{i=1..omega(n)} i*p_i, where {p_i}, i=1..omega(n) is the increasing sequence of prime divisors of n, where omega is the number of distinct prime factors of n (A001221).

0, 2, 3, 2, 5, 8, 7, 2, 3, 12, 11, 8, 13, 16, 13, 2, 17, 8, 19, 12, 17, 24, 23, 8, 5, 28, 3, 16, 29, 23, 31, 2, 25, 36, 19, 8, 37, 40, 29, 12, 41, 29, 43, 24, 13, 48, 47, 8, 7, 12, 37, 28, 53, 8, 27, 16, 41, 60, 59, 23, 61, 64, 17, 2, 31, 41, 67, 36, 49, 33, 71, 8, 73, 76, 13, 40

Offset: 1

Author

Vladeta Jovovic, Oct 27 2001

Keywords

• nonn

Examples

			factorset(30) = {2,3,5}, thus a(30) = 1*2 + 2*3 + 3*5 = 23.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001221 (omega).

Programs

Maple

with(numtheory): seq(add(i*sort(convert(factorset(n),'list'))[i],i=1..nops(factorset(n))), n=1..200);

Mathematica

ispd[n_]:=Module[{f=FactorInteger[n][[All,1]]},Total[f Range[ Length[f]]]]; Join[{0},Array[ispd,80,2]] (* Harvey P. Dale, Aug 06 2017 *)

PARI

{ for (n=1, 1000, f=factor(n)~; a=sum(i=1, length(f), i*f[1, i]); write("b064939.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 30 2009

Formula

a(n) = Sum_{p|n, q|n, p and q prime, p <= q} q. - Wesley Ivan Hurt, Aug 20 2020