A242899 - OEIS

%I #19 Jun 03 2021 12:32:42

%S 2,2,3,4,3,3,3,2,3,6,8,4,11,5,3,16,7,6,5,5,3,10,5,3,4,5,3,4,11,4,7,11,

%T 3,30,5,3,7,19,3,10,7,6,7,11,5,12,14,6,7,5,3,12,13,9,5,8,6,6,11,4,4,6,

%U 3,64,5,6,10,6,3,10,6,6,5,37,3,30,7,12,7,20,3,40,19,9

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

%C a(n) <= n for all n > 1.

%H Seiichi Manyama, <a href="/A242899/b242899.txt">Table of n, a(n) for n = 1..10000</a>

%e (1^2+2^1)/(2+1) = 3/3 = 1 is an integer. Thus a(1) = 2.

%t lnk[n_]:=Module[{k=2},While[!IntegerQ[(n^k+k^n)/(k+n)],k++];k]; Array[lnk,90] (* _Harvey P. Dale_, Sep 02 2015 *)

%o (PARI) a(n)=if(n==1, 2, for(k=2, n, s=(n^k+k^n)/(k+n); if(floor(s)==s, return(k))))

%o n=1; while(n<100, print(a(n)); n+=1)

%o (PARI) a(n) = my(k=2); while (denominator((n^k+k^n)/(k+n))!=1, k++); k; \\ _Michel Marcus_, Jun 03 2021

%Y Cf. A114977, A114978, A242872.

%K nonn,look

%O 1,1

%A _Derek Orr_, May 25 2014