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A259111 a(n) = least number k > 1 such that 1^k + 2^k + ... + k^k == n (mod k). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 11 15:49 EDT 2021. Contains 342886 sequences. (Running on oeis4.)