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.

A356238 a(n) = Sum_{k=1..n} (k * floor(n/k))^n.

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%I A356238 #18 Aug 02 2022 10:37:59
%S A356238 1,8,62,849,8541,206345,2581403,76623522,1617299079,49463993875,
%T A356238 952905453423,59000021366675,1198427462876421,54128102218676115,
%U A356238 2321105129608323165,117387839988330848902,3205342976298888473968,268263812478494295219717
%N A356238 a(n) = Sum_{k=1..n} (k * floor(n/k))^n.
%H A356238 Seiichi Manyama, <a href="/A356238/b356238.txt">Table of n, a(n) for n = 1..386</a>
%F A356238 a(n) = Sum_{k=1..n} k^n * Sum_{d|k} (1 - (1 - 1/d)^n).
%t A356238 a[n_] := Sum[(k * Floor[n/k])^n, {k, 1, n}]; Array[a, 18] (* _Amiram Eldar_, Jul 30 2022 *)
%o A356238 (PARI) a(n) = sum(k=1, n, (k*(n\k))^n);
%o A356238 (PARI) a(n) = sum(k=1, n, k^n*sumdiv(k, d, 1-(1-1/d)^n));
%Y A356238 Cf. A007778, A350109, A350125, A356239, A356240.
%K A356238 nonn
%O A356238 1,2
%A A356238 _Seiichi Manyama_, Jul 30 2022