A259111 a(n) = least number k > 1 such that 1^k + 2^k + ... + k^k == n (mod k).

2, 4, 2, 8, 2, 3, 2, 16, 2, 4, 2, 3, 2, 4, 2, 32, 2, 3, 2, 5, 2, 4, 2, 3, 2, 4, 2, 7, 2, 3, 2, 64, 2, 4, 2, 3, 2, 4, 2, 5, 2, 3, 2, 8, 2, 4, 2, 3, 2, 4, 2, 8, 2, 3, 2, 7, 2, 4, 2, 3, 2, 4, 2, 128, 2, 3, 2, 8, 2, 4, 2, 3, 2, 4, 2, 8, 2, 3, 2, 5, 2, 4, 2, 3, 2, 4, 2, 11, 2, 3, 2, 8, 2, 4, 2, 3, 2, 4, 2, 5

Offset: 1

Author

Derek Orr, Jun 18 2015

Keywords

• nonn

Examples

			Consider n=2:
Is k=2? 1^2 + 2^2 == 1 (mod 2). No.
Is k=3? 1^3 + 2^3 + 3^3 == 0 (mod 3). No.
Is k=4? 1^4 + 2^4 + 3^4 + 4^4 == 2 (mod 4). Yes. So a(2) = 4.
(Example corrected by _N. J. A. Sloane_, Jul 02 2019)
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..8192

Crossrefs

Cf. A014117, A226960-A226967.

Programs

Maple

a:= proc(n) local k; for k from 2 while
      add(i&^k mod k, i=1..k) mod k <> n mod k do od; k
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Jun 18 2015

Mathematica

lnk[n_]:=Module[{k=2},While[Mod[Total[Range[k]^k],k]!=Mod[n,k],k++];k]; Array[ lnk,100] (* Harvey P. Dale, Jul 02 2019 *)

PARI

vector(100,n,k=2;while(sum(i=1,k,i^k)!=Mod(n,k),k++);k)

Formula

a(2^n) = 2^(n+1) for n >= 0.