A242801 - OEIS

%I #19 Jun 04 2021 09:42:21

%S 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 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 16,16,9,10,7,16,13,16,6,17,9,13,5,16,5,9,7,13,7,4,9,41,15

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

%C It is believed that a(n) <= n+2 for all n > 0.

%C a(n) also exists for all n < 1. - _Robert G. Wilson v_, Jun 05 2014

%H Seiichi Manyama, <a href="/A242801/b242801.txt">Table of n, a(n) for n = 1..10000</a>

%e (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 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 (PARI) a(n)=for(k=2,1000,s=(k^k+n)/(k+n);if(floor(s)==s,return(k)));

%o n=1;while(n<100,print(a(n), ", ");n+=1) \\ corrected by _Michel Marcus_, May 24 2014

%Y Cf. A213382, A242800.

%K nonn

%O 1,1

%A _Derek Orr_, May 23 2014