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A242801 Least number k > 1 such that (k^k+n)/(k+n) is an integer.

%I A242801 #19 Jun 04 2021 09:42:21
%S A242801 3,4,3,6,3,8,5,4,3,4,5,7,11,4,5,18,4,20,5,8,3,11,9,4,5,13,9,16,7,19,7,
%T A242801 4,11,5,5,7,19,4,9,16,7,9,5,6,15,16,5,8,7,7,9,13,19,12,5,7,12,29,4,5,
%U A242801 16,16,9,10,7,16,13,16,6,17,9,13,5,16,5,9,7,13,7,4,9,41,15
%N A242801 Least number k > 1 such that (k^k+n)/(k+n) is an integer.
%C A242801 It is believed that a(n) <= n+2 for all n > 0.
%C A242801 a(n) also exists for all n < 1. - _Robert G. Wilson v_, Jun 05 2014
%H A242801 Seiichi Manyama, <a href="/A242801/b242801.txt">Table of n, a(n) for n = 1..10000</a>
%e A242801 (2^2+1)/(2+1) = 5/3 is not an integer. (3^3+1)/(3+1) = 28/4 = 7 is an integer. Thus a(1) = 3.
%t A242801 f[n_] := Block[{k = 2}, While[ Mod[ PowerMod[k, k, k + n] + n, k + n] != 0, k++]; k]; Array[f, 90] (* _Robert G. Wilson v_, Jun 05 2014 *)
%o A242801 (PARI) a(n)=for(k=2,1000,s=(k^k+n)/(k+n);if(floor(s)==s,return(k)));
%o A242801 n=1;while(n<100,print(a(n), ", ");n+=1) \\ corrected by _Michel Marcus_, May 24 2014
%Y A242801 Cf. A213382, A242800.
%K A242801 nonn
%O A242801 1,1
%A A242801 _Derek Orr_, May 23 2014