A242789 Least number k > 1 such that (k^k-n)/(k-n) is an integer.

2, 3, 2, 2, 3, 3, 3, 4, 3, 4, 3, 6, 4, 7, 3, 4, 5, 4, 7, 5, 5, 4, 7, 9, 4, 7, 3, 7, 5, 13, 5, 4, 9, 12, 5, 6, 10, 16, 9, 4, 9, 16, 7, 5, 5, 4, 10, 13, 7, 7, 11, 13, 5, 9, 7, 6, 5, 12, 19, 9, 11, 17, 7, 7, 5, 11, 4, 16, 9, 5, 11, 16, 9, 13, 15, 13, 9, 12, 7, 31, 6, 16, 5

Offset: 1

Author

Derek Orr, May 22 2014

Keywords

• nonn

Comments

a(n) <= n+1 for all n.

Examples

			(2^2-8)/(2-8) = -4/-6 is not an integer. (3^3-8)/(3-8) = 19/-5 is not an integer. (4^4-8)/(4-8) = 248/4 = 62 is an integer. Thus a(8) = 4.
		

Links

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

Crossrefs

Cf. A242787, A242788.

Programs

Mathematica

a[n_] := Module[{k = 2}, While[k == n || ! Divisible[k^k - n, k - n], k++]; k]; Array[a, 100] (* Amiram Eldar, Jun 04 2021 *)

PARI

a(n)=for(k=2,n+1,if(k!=n,s=(k^k-n)/(k-n);if(floor(s)==s,return(k))));
n=1;while(n<100,print(a(n));n+=1)