A347718 a(n) = Sum of the divisors of sigma_n(n).

1, 6, 56, 448, 6264, 96348, 1559520, 16908804, 391945400, 20553536052, 706019328000, 20210523379200, 519285252355776, 21710734431216480, 1456143373228677120, 25536237889612326912, 1792353900753729655758, 52839150354952425838080, 4154723599066412190910560

Offset: 1

Author

Wesley Ivan Hurt, Jan 28 2022

Keywords

• nonn

Examples

			a(3) = sigma(sigma_3(3)) = sigma(1^3+3^3) = sigma(28) = 1+2+4+7+14+28 = 56.
		

Links

• Daniel Suteu, Table of n, a(n) for n = 1..120 (first 42 terms from Chai Wah Wu)
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A023887, A064165.

Programs

Maple

a:= n-> (s-> s(s[n](n)))(numtheory[sigma]):
seq(a(n), n=1..20);  # Alois P. Heinz, Jan 28 2022

Mathematica

Table[DivisorSigma[1, DivisorSigma[n, n]], {n, 20}]

Python

from math import prod
from collections import Counter
from sympy import factorint
def A347718(n): return prod((q**(r+1)-1)//(q-1) for q,r in sum((Counter(factorint((p**(n*(e+1))-1)//(p**n-1))) for p, e in factorint(n).items()),Counter()).items()) # Chai Wah Wu, Jan 28 2022

Formula

a(n) = sigma(sigma_n(n)).

a(n) = A000203(A023887(n)). - Michel Marcus, Jan 29 2022