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

1,1

Links

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

Formula

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

Example

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)

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 *)

Prog

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

Crossrefs

Cf. A014117, A226960-A226967.

Sequence in context: A335573 A073017 A296092 * A209675 A307669 A171977

Adjacent sequences: A259108 A259109 A259110 * A259112 A259113 A259114

Keyword

nonn

Author

Derek Orr, Jun 18 2015

Status

approved