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.

A308763 a(n) = Sum_{d|n} d^(n-2).

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%I A308763 #23 May 08 2021 06:26:33
%S A308763 1,2,4,21,126,1394,16808,266305,4785157,100390882,2357947692,
%T A308763 61978939050,1792160394038,56707753666594,1946196290656824,
%U A308763 72061992352890881,2862423051509815794,121441386937936123331,5480386857784802185940,262145000003883417004506
%N A308763 a(n) = Sum_{d|n} d^(n-2).
%H A308763 Seiichi Manyama, <a href="/A308763/b308763.txt">Table of n, a(n) for n = 1..388</a>
%F A308763 L.g.f.: -log(Product_{k>=1} (1 - (k*x)^k)^(1/k^3)) = Sum_{k>=1} a(k)*x^k/k.
%F A308763 G.f.: Sum_{k>=1} k^(k-2) * x^k/(1 - (k*x)^k).
%t A308763 a[n_] := DivisorSum[n, #^(n - 2) &]; Array[a, 20] (* _Amiram Eldar_, May 08 2021 *)
%o A308763 (PARI) {a(n) = sigma(n, n-2)}
%o A308763 (PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-(k*x)^k)^(1/k^3)))))
%o A308763 (PARI) N=20; x='x+O('x^N); Vec(sum(k=1, N, k^(k-2)*x^k/(1-(k*x)^k)))
%Y A308763 Cf. A023887, A082245, A294645, A294810, A308755.
%K A308763 nonn
%O A308763 1,2
%A A308763 _Seiichi Manyama_, Jun 23 2019