A193526 Sum of even divisors of sopf(n).

0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 14, 2, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 2, 16, 0, 24, 0, 0, 0, 30, 0, 0, 24, 0, 0, 14, 0, 0, 0, 0, 0, 36, 0, 0, 0, 30, 0, 24, 0, 0, 12, 0, 0, 12, 2, 26, 30, 0, 0, 28, 16, 0, 0, 0, 0, 14, 0, 26, 26, 0, 0

Offset: 1

Author

Michel Lagneau, Jul 29 2011

Keywords

• nonn
• easy

Comments

Sopf(n) is the sum of the distinct primes dividing n (A008472).

Links

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

Crossrefs

Cf. A008472, A146076, A193525.

Programs

Mathematica

Table[Total[Select[Divisors[Plus @@ First[Transpose[FactorInteger[n]]]], EvenQ[#] &]], {n, 100}]

PARI

A008472(n) = vecsum(factor(n)[, 1]); \\ From A008472
A146076(n) = if (n%2, 0, 2*sigma(n/2)); \\ From A146076
A193526(n) = if(1==n,0,A146076(A008472(n))); \\ Antti Karttunen, Dec 23 2018

Formula

a(1) = 0; for n > 1, a(n) = A146076(A008472(n)). - Antti Karttunen, Dec 23 2018