A330526 a(n) = (p-1)! mod p^3, where p = prime(n).
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
Offset: 1
Keywords
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.
Programs
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Magma
[Factorial(p-1)mod p^3: p in PrimesUpTo(170)]; // Marius A. Burtea, Dec 18 2019
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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 -
Mathematica
Mod[(#-1)!,#^3]&/@Prime[Range[40]] (* Harvey P. Dale, Jan 09 2024 *)
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PARI
a(n) = my(p=prime(n)); (p-1)! % p^3;