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

1,1

Comments

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

Links

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

Example

(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.

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 *)

Prog

(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)

Crossrefs

Cf. A242787, A242788.

Sequence in context: A256170 A051686 A079294 * A366712 A366713 A076733

Adjacent sequences: A242786 A242787 A242788 * A242790 A242791 A242792

Keyword

nonn

Author

Derek Orr, May 22 2014

Status

approved