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.

A308670 a(n) = Sum_{d|n} d^(d*n).

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%I A308670 #18 May 11 2021 01:54:24
%S A308670 1,17,19684,4294967553,298023223876953126,
%T A308670 10314424798490535546559373642,
%U A308670 256923577521058878088611477224235621321608,6277101735386680763835789423207666416120802188537744130049
%N A308670 a(n) = Sum_{d|n} d^(d*n).
%F A308670 L.g.f.: -log(Product_{k>=1} (1 - (k^k*x)^k)^(1/k)) = Sum_{k>=1} a(k)*x^k/k.
%t A308670 a[n_] := DivisorSum[n, #^(#*n) &]; Array[a, 8] (* _Amiram Eldar_, May 11 2021 *)
%o A308670 (PARI) {a(n) = sumdiv(n, d, d^(d*n))}
%o A308670 (PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-(k^k*x)^k)^(1/k)))))
%Y A308670 Column k=2 of A308676.
%Y A308670 Cf. A023887, A062796, A308571, A308671, A308675.
%K A308670 nonn
%O A308670 1,2
%A A308670 _Seiichi Manyama_, Jun 16 2019