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.

A294810 a(n) = Sum_{d|n} d^(n+2).

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%I A294810 #17 Dec 23 2023 18:02:51
%S A294810 1,17,244,4161,78126,1686434,40353608,1074791425,31381236757,
%T A294810 1000244144722,34522712143932,1283997101947770,51185893014090758,
%U A294810 2177986570740006274,98526126098761952664,4722384497336874434561,239072435685151324847154
%N A294810 a(n) = Sum_{d|n} d^(n+2).
%H A294810 Seiichi Manyama, <a href="/A294810/b294810.txt">Table of n, a(n) for n = 1..384</a>
%F A294810 G.f.: Sum_{k>0} k^(k+2)*x^k/(1-(k*x)^k).
%F A294810 L.g.f.: -log(Product_{k>=1} (1 - (k*x)^k)^k) = Sum_{k>=1} a(k)*x^k/k. - _Seiichi Manyama_, Jun 02 2019
%t A294810 Table[Total[Divisors[n]^(n+2)],{n,20}] (* _Harvey P. Dale_, Dec 23 2023 *)
%o A294810 (PARI) {a(n) = sigma(n, n+2)}
%o A294810 (PARI) N=66; x='x+O('x^N); Vec(sum(k=1, N, k^(k+2)*x^k/(1-(k*x)^k)))
%o A294810 (PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-(k*x)^k)^k)))) \\ _Seiichi Manyama_, Jun 02 2019
%Y A294810 Cf. A294645, A294809.
%K A294810 nonn
%O A294810 1,2
%A A294810 _Seiichi Manyama_, Nov 09 2017