cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A307794 a(1) = 1; a(n+1) = Sum_{d|n} sigma(d)*a(d), where sigma = sum of divisors (A000203).

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%I A307794 #9 Apr 29 2019 20:37:09
%S A307794 1,1,4,17,123,739,8888,71105,1066698,13867091,249608380,2995300561,
%T A307794 83868424715,1174157946011,28179790775372,676314978609683,
%U A307794 20965764337966871,377383758083403679,14717966565266619443,294359331305332388861,12363091914824209940661,395618941274374718172273
%N A307794 a(1) = 1; a(n+1) = Sum_{d|n} sigma(d)*a(d), where sigma = sum of divisors (A000203).
%F A307794 G.f.: x * (1 + Sum_{n>=1} sigma(n)*a(n)*x^n/(1 - x^n)).
%F A307794 L.g.f.: -log(Product_{i>=1, j>=1} (1 - x^(i*j))^(a(i*j)/j)) = Sum_{n>=1} a(n+1)*x^n/n.
%t A307794 a[n_] := a[n] = Sum[DivisorSigma[1, d] a[d], {d, Divisors[n - 1]}]; a[1] = 1; Table[a[n], {n, 1, 22}]
%t A307794 a[n_] := a[n] = SeriesCoefficient[x (1 + Sum[DivisorSigma[1, k] a[k] x^k/(1 - x^k), {k, 1, n - 1}]), {x, 0, n}]; Table[a[n], {n, 1, 22}]
%o A307794 (PARI) a(n) = if (n==1, 1, sumdiv(n-1, d, sigma(d)*a(d))); \\ _Michel Marcus_, Apr 29 2019
%Y A307794 Cf. A000203, A001001, A307793.
%K A307794 nonn
%O A307794 1,3
%A A307794 _Ilya Gutkovskiy_, Apr 29 2019