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

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

Offset: 1

Author

Derek Orr, May 23 2014

Keywords

• nonn

Comments

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

a(n) also exists for all n < 1. - Robert G. Wilson v, Jun 05 2014

Examples

			(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.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A213382, A242800.

Programs

Mathematica

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 *)

PARI

a(n)=for(k=2,1000,s=(k^k+n)/(k+n);if(floor(s)==s,return(k)));
n=1;while(n<100,print(a(n), ", ");n+=1) \\ corrected by Michel Marcus, May 24 2014