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A317058 a(n) is the smallest composite k such that 1^(k-1) + 2^(k-1) + ... + n^(k-1) == n (mod k). 6
4, 341, 473, 4, 4, 133, 497, 4, 4, 15, 9, 4, 4, 143, 35, 4, 4, 51, 57, 4, 4, 77, 253, 4, 4, 65, 9, 4, 4, 115, 155, 4, 4, 187, 35, 4, 4, 9, 247, 4, 4, 287, 2051, 4, 4, 15, 33, 4, 4, 35, 85, 4, 4, 9, 9, 4, 4, 551, 1711, 4, 4, 713, 21, 4, 4, 55, 77, 4, 4, 35, 35, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

According to the Agoh-Giuga conjecture, a(n) <> n+1.

a(n) = 4 if and only if n == {0, 1} (mod 4).

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..9661 (n = 1..500 from Seiichi Manyama)

Wikipedia, Agoh-Giuga conjecture

MATHEMATICA

a[n_] := Block[{k = 4}, While[PrimeQ[k] || Mod[Sum[PowerMod[j, k-1, k], {j, n}], k] != Mod[n, k], k++]; k]; Array[a, 72] (* Giovanni Resta, Jul 26 2018 *)

PROG

(PARI) a(n) = forcomposite(k=1, , if (sum(j=1, n, Mod(j, k)^(k-1)) == n, return (k)); ); \\ Michel Marcus, Jul 26 2018

(Python)

from sympy import isprime

def g(n, p, q): # compute (-n + sum_{k=1, n} k^p)  mod q

    c = (-n) % q

    for k in range(1, n+1):

        c = (c+pow(k, p, q)) % q

    return c

def A317058(n):

    k = 2

    while isprime(k) or g(n, k-1, k):

        k += 1

    return k # Chai Wah Wu, Jul 30 2018

CROSSREFS

Cf. A000790, A133906, A133907, A317357, A317358.

Sequence in context: A007535 A000783 A098654 * A317357 A069884 A332134

Adjacent sequences:  A317055 A317056 A317057 * A317059 A317060 A317061

KEYWORD

nonn

AUTHOR

Thomas Ordowski, Jul 26 2018

EXTENSIONS

More terms from Giovanni Resta, Jul 26 2018

STATUS

approved

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Last modified July 4 11:31 EDT 2020. Contains 335448 sequences. (Running on oeis4.)