A367131 a(n) is the sum of the divisors of A000058(n) (Sylvester's sequence).

3, 4, 8, 44, 1960, 3263444, 10697794573312, 113429214231136770625234912, 12864938683281101589385656009398714729057117020127552, 166504803622354833425112235578181474001920862856209391632362182416351065666575351284563698791731209336320

Offset: 0

Author

Sean A. Irvine, Nov 05 2023

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10
• Wikipedia, Sylvester's sequence: Divisibility and factorizations.

Crossrefs

Cf. A000058, A000203, A091335, A367130.

Programs

Mathematica

a000058[0] = 2; a000058[n_Integer?NonNegative] := a000058[n] = a000058[n - 1]^2 - a000058[n - 1] + 1; a[n_Integer?NonNegative] := a[n] = DivisorSigma[1, a000058[n]]; Table[a[n], {n, 0, 9}] (* Robert P. P. McKone, Nov 05 2023 *)

Python

from sympy import divisor_sigma
memo = {0: 2}
def a000058(n):
    if n not in memo:
        memo[n] = a000058(n - 1)**2 - a000058(n - 1) + 1
    return memo[n]
a = lambda n: divisor_sigma(a000058(n))
print([a(n) for n in range(10)])
# Robert P. P. McKone, Nov 05 2023

Formula

a(n) = sigma(A000058(n)) = A000203(A000058(n)).