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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.)