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

%I A367131 #13 Oct 29 2024 03:57:48
%S A367131 3,4,8,44,1960,3263444,10697794573312,113429214231136770625234912,
%T A367131 12864938683281101589385656009398714729057117020127552,
%U A367131 166504803622354833425112235578181474001920862856209391632362182416351065666575351284563698791731209336320
%N A367131 a(n) is the sum of the divisors of A000058(n) (Sylvester's sequence).
%H A367131 Amiram Eldar, <a href="/A367131/b367131.txt">Table of n, a(n) for n = 0..10</a>
%H A367131 Wikipedia, <a href="https://en.wikipedia.org/wiki/Sylvester%27s_sequence#Divisibility_and_factorizations">Sylvester's sequence: Divisibility and factorizations</a>.
%F A367131 a(n) = sigma(A000058(n)) = A000203(A000058(n)).
%t A367131 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 *)
%o A367131 (Python)
%o A367131 from sympy import divisor_sigma
%o A367131 memo = {0: 2}
%o A367131 def a000058(n):
%o A367131     if n not in memo:
%o A367131         memo[n] = a000058(n - 1)**2 - a000058(n - 1) + 1
%o A367131     return memo[n]
%o A367131 a = lambda n: divisor_sigma(a000058(n))
%o A367131 print([a(n) for n in range(10)])
%o A367131 # _Robert P. P. McKone_, Nov 05 2023
%Y A367131 Cf. A000058, A000203, A091335, A367130.
%K A367131 nonn
%O A367131 0,1
%A A367131 _Sean A. Irvine_, Nov 05 2023