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.

A308756 a(n) = Sum_{d|n} d^(2*(d-2)).

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%I A308756 #19 May 08 2021 06:26:21
%S A308756 1,2,10,258,15626,1679627,282475250,68719476994,22876792454971,
%T A308756 10000000000015627,5559917313492231482,3833759992447476802059,
%U A308756 3211838877954855105157370,3214199700417740937033562867,3787675244106352329254150406260
%N A308756 a(n) = Sum_{d|n} d^(2*(d-2)).
%H A308756 Seiichi Manyama, <a href="/A308756/b308756.txt">Table of n, a(n) for n = 1..216</a>
%F A308756 L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^(2*k-5))) = Sum_{k>=1} a(k)*x^k/k.
%F A308756 G.f.: Sum_{k>=1} k^(2*(k-2)) * x^k/(1 - x^k).
%t A308756 a[n_] := DivisorSum[n, #^(2*(# - 2)) &]; Array[a, 15] (* _Amiram Eldar_, May 08 2021 *)
%o A308756 (PARI) {a(n) = sumdiv(n, d, d^(2*(d-2)))}
%o A308756 (PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-x^k)^k^(2*k-5)))))
%o A308756 (PARI) N=20; x='x+O('x^N); Vec(sum(k=1, N, k^(2*(k-2))*x^k/(1-x^k)))
%Y A308756 Cf. A283533, A308696.
%K A308756 nonn
%O A308756 1,2
%A A308756 _Seiichi Manyama_, Jun 22 2019