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.

A308755 a(n) = Sum_{d|n} d^(d-2).

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%I A308755 #19 May 08 2021 06:26:25
%S A308755 1,2,4,18,126,1301,16808,262162,4782973,100000127,2357947692,
%T A308755 61917365541,1792160394038,56693912392105,1946195068359504,
%U A308755 72057594038190098,2862423051509815794,121439531096599036046,5480386857784802185940,262144000000000100000143
%N A308755 a(n) = Sum_{d|n} d^(d-2).
%H A308755 Seiichi Manyama, <a href="/A308755/b308755.txt">Table of n, a(n) for n = 1..388</a>
%F A308755 L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^(k-3))) = Sum_{k>=1} a(k)*x^k/k.
%F A308755 G.f.: Sum_{k>=1} k^(k-2) * x^k/(1 - x^k).
%t A308755 a[n_] := DivisorSum[n, #^(# - 2) &]; Array[a, 20] (* _Amiram Eldar_, May 08 2021 *)
%o A308755 (PARI) {a(n) = sumdiv(n, d, d^(d-2))}
%o A308755 (PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-x^k)^k^(k-3)))))
%o A308755 (PARI) N=20; x='x+O('x^N); Vec(sum(k=1, N, k^(k-2)*x^k/(1-x^k)))
%Y A308755 Cf. A062796, A262843, A283498, A308753.
%K A308755 nonn
%O A308755 1,2
%A A308755 _Seiichi Manyama_, Jun 22 2019