A080649 Sum of prime factors of sigma(n).

3, 2, 7, 5, 5, 2, 8, 13, 5, 5, 9, 9, 5, 5, 31, 5, 16, 7, 12, 2, 5, 5, 10, 31, 12, 7, 9, 10, 5, 2, 10, 5, 5, 5, 20, 21, 10, 9, 10, 12, 5, 13, 12, 18, 5, 5, 33, 22, 34, 5, 9, 5, 10, 5, 10, 7, 10, 10, 12, 33, 5, 15, 127, 12, 5, 19, 12, 5, 5, 5, 21, 39, 24, 33, 14, 5, 12, 7, 36, 11, 12, 12, 9, 5

Offset

2,1

Links

Indranil Ghosh, Table of n, a(n) for n = 2..10000

Formula

a(n) = A008472(A000203(n)). - Indranil Ghosh, Jan 13 2017

Example

For n = 10, sigma(10) = 18 and the sum of the prime factors of 18 is 2 + 3 = 5. So, a(10) = 5. - Indranil Ghosh, Jan 13 2017

Mathematica

Table[Apply[Plus, Transpose[FactorInteger[DivisorSigma[1, n]]][[1]]], {n, 3, 100}]

Prog

(Python)
from sympy import isprime
def sigma(n):
    return sum(i for i in range(1, n+1) if n % i == 0)
def sopf(n):
    return sum(i for i in range(1, n+1) if n % i == 0 and isprime(i))
def A080649(n):
    return sopf(sigma(n))
for i in range(2, 101):
    print(str(i)+" "+str(A080649(i))) # Indranil Ghosh, Jan 15 2017
(PARI) a(n) = vecsum(factor(sigma(n))[, 1]); \\ Michel Marcus, Jan 14 2017

Crossrefs

Cf. A000203, A008472.

Sequence in context: A191447 A191538 A361876 * A130839 A366565 A082318

Adjacent sequences: A080646 A080647 A080648 * A080650 A080651 A080652

Keyword

nonn

Author

Joseph L. Pe, Feb 28 2003

Status

approved