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.

A119758 Numerator of Sum_{k=1..n} k^n/n^k.

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%I A119758 #9 May 31 2022 11:23:13
%S A119758 1,3,20,225,3789,89341,2821552,115377921,5939637425,375840753541,
%T A119758 28641787322796,2583828842108449,271949027324094925,
%U A119758 32986652806128680205,4563200871898056653504,713455071424061222336513
%N A119758 Numerator of Sum_{k=1..n} k^n/n^k.
%C A119758 a(p-1) is divisible by prime p>2. a(p) is divisible by ((p+1)/2)^2 for prime p>2.
%C A119758 Denominator of Sum[k^n/n^k,{k,1,n}] is equal to n^(n-1) = A000169(n). - _Alexander Adamchuk_, Jun 27 2006
%F A119758 a(n) = numerator(Sum_{k=1..n} k^n/n^k).
%F A119758 a(n) = n^(n-1)*(Sum_{k=1..n} k^n/n^k). - _Alexander Adamchuk_, Jun 27 2006
%F A119758 a(2m) is divisible by 2m+1 for integer m>0. a(2m-1) is divisible by m^2 for integer m>0. - _Alexander Adamchuk_, Jun 27 2006
%t A119758 Table[Numerator[Sum[k^n/n^k,{k,1,n}]],{n,1,20}]
%t A119758 Table[Sum[k^n/n^k,{k,1,n}]*n^(n-1),{n,1,50}] (* _Alexander Adamchuk_, Jun 27 2006 *)
%o A119758 (PARI) a(n) = numerator(prod(k=2, n, 1-1/(prime(k)-1)^2)); \\ _Michel Marcus_, May 31 2022
%Y A119758 Cf. A023037, A031971.
%Y A119758 Cf. A000169.
%K A119758 frac,nonn
%O A119758 1,2
%A A119758 _Alexander Adamchuk_, Jun 18 2006, Jun 25 2006