A085020 a(n) = Sum_{d|n, (d+1) prime} (d + 1).

2, 5, 2, 10, 2, 12, 2, 10, 2, 16, 2, 30, 2, 5, 2, 27, 2, 31, 2, 21, 2, 28, 2, 30, 2, 5, 2, 39, 2, 54, 2, 27, 2, 5, 2, 86, 2, 5, 2, 62, 2, 55, 2, 33, 2, 52, 2, 47, 2, 16, 2, 63, 2, 31, 2, 39, 2, 64, 2, 133, 2, 5, 2, 27, 2, 102, 2, 10, 2, 87, 2, 159, 2, 5, 2, 10, 2, 91, 2, 79, 2, 88, 2, 102, 2, 5

Offset: 1

Author

Jason Earls, Jun 18 2003

Keywords

• easy
• nonn

Examples

			a(18) = 31 because the divisors of 18 are [1, 2, 3, 6, 9, 18] and 2 + 3 + 7 + 19 = 31.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A067513.

Cf. A008472. [Peter Luschny, May 04 2009]

Programs

Maple

T := proc(n,k) local i; numtheory[divisors](n); select(isprime, map(i->i+k, %)); add(i,i=%) end: seq(T(n+1,1),n=0..20); # Peter Luschny, May 04 2009

Mathematica

a[n_] := Sum[If[PrimeQ[d+1], d+1, 0], {d, Divisors[n]}]; Array[a, 100] (* Jean-François Alcover, Jun 04 2019 *)

PARI

a(n) = sumdiv(n, d, if (isprime(q=d+1), q)); \\ Michel Marcus, Aug 14 2017