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A330526 a(n) = (p-1)! mod p^3, where p = prime(n). 1
1, 2, 24, 34, 494, 675, 4419, 4008, 4944, 13136, 21730, 23531, 14103, 41236, 86432, 77644, 64250, 148534, 243209, 141005, 384490, 373985, 29215, 101281, 543102, 109281, 154396, 1122108, 965630, 1006716, 1283207, 152876, 2147337, 1419745, 1545874, 1381045, 1108262, 123879 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

Claire Levaillant, Wilson's theorem modulo p^2 derived from Faulhaber polynomials, arXiv:1912.06652 [math.CO], 2019.

Zhi-Hong Sun, Congruences concerning Bernoulli numbers and Bernoulli polynomials, Discrete Applied Math. 105 (2000) 193 - 223.

FORMULA

a(n)= A177771(n) mod A030078(n).

MAPLE

f:= proc(n) local p, p3, k, r;

    p:= ithprime(n);

    p3:= p^3;

    r:= 1:

    for k from 1 to p-1 do

      r:= r*k mod p3

    od;

    r

end proc:

map(f, [$1..100]); # Robert Israel, Dec 18 2019

PROG

(PARI) a(n) = my(p=prime(n)); (p-1)! % p^3;

(MAGMA) [Factorial(p-1)mod p^3: p in PrimesUpTo(170)]; // Marius A. Burtea, Dec 18 2019

CROSSREFS

Cf. A030078, A112660, A177771.

Sequence in context: A139334 A212759 A112660 * A280648 A119066 A019996

Adjacent sequences:  A330523 A330524 A330525 * A330527 A330528 A330529

KEYWORD

nonn

AUTHOR

Michel Marcus, Dec 17 2019

STATUS

approved

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Last modified October 25 19:28 EDT 2020. Contains 338012 sequences. (Running on oeis4.)