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

1,1

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

Links

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

Example

(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.

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 *)

Prog

(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

Crossrefs

Cf. A213382, A242800.

Sequence in context: A281626 A327650 A338128 * A021295 A061112 A078809

Adjacent sequences: A242798 A242799 A242800 * A242802 A242803 A242804

Keyword

nonn

Author

Derek Orr, May 23 2014

Status

approved