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