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.

A356240 a(n) = Sum_{k=1..n} (k-1)^n * Sum_{j=1..floor(n/k)} j^n.

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%I A356240 #17 Jul 30 2022 14:14:16
%S A356240 0,1,9,114,1332,25404,395460,9724901,207584371,6120938951,
%T A356240 151737244257,5932533980409,168400694345669,7145593797561899,
%U A356240 260681076993636793,12410128414690753548,473029927456547840472,27572016889372245275679
%N A356240 a(n) = Sum_{k=1..n} (k-1)^n * Sum_{j=1..floor(n/k)} j^n.
%F A356240 a(n) = Sum_{k=1..n} k^n * (sigma_0(k) - floor(n/k)^n) = A356239(n) - A356238(n).
%F A356240 a(n) = Sum_{k=1..n} k^n * Sum_{d|k} (1 - 1/d)^n.
%t A356240 a[n_] := Sum[(k - 1)^n * Sum[j^n, {j, 1, Floor[n/k]}], {k, 1, n}]; Array[a, 18] (* _Amiram Eldar_, Jul 30 2022 *)
%o A356240 (PARI) a(n) = sum(k=1, n, (k-1)^n*sum(j=1, n\k, j^n));
%o A356240 (PARI) a(n) = sum(k=1, n, k^n*(sigma(k, 0)-(n\k)^n));
%o A356240 (PARI) a(n) = sum(k=1, n, k^n*sumdiv(k, d, (1-1/d)^n));
%Y A356240 Cf. A356131, A356238, A356239, A356244.
%K A356240 nonn
%O A356240 1,3
%A A356240 _Seiichi Manyama_, Jul 30 2022