A175624 a(n) = n! modulo n*(n+1)*(n+2)/3.

1, 2, 6, 24, 50, 48, 0, 0, 210, 120, 352, 168, 0, 0, 800, 288, 1122, 360, 0, 0, 2002, 528, 0, 0, 0, 0, 4032, 840, 4930, 960, 0, 0, 0, 0, 8400, 1368, 0, 0, 11440, 1680, 13202, 1848, 0, 0, 17250, 2208, 0, 0, 0, 0, 24752, 2808, 0, 0, 0, 0, 34162, 3480, 37760, 3720, 0, 0, 0, 0

Offset: 1

Author

John W. Layman, Jul 27 2010

Keywords

• nonn

Comments

It appears that a(1)=1, a(2)=2, a(3)=6, and, for n>3, a(n) = n*(n+2) if n+1 is prime, else a(n) = n*(n+1)*(n+5)/6 if n+2 is prime, else a(n)=0. This has been verified for n up to 1000.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A061006, A072230, A119690, A120387, A175567.

Programs

Magma

[Factorial(n) mod (2*Binomial(n+2,3)): n in [1..80]]; // G. C. Greubel, Apr 12 2024

Mathematica

Table[Mod[(n!), (n^3 + 3 n^2 + 2 n)/3], {n, 100}] (* Vincenzo Librandi, Jul 10 2014 *)

PARI

a(n) = n! % (n*(n+1)*(n+2)/3); \\ Michel Marcus, Jul 09 2014

SageMath

[factorial(n)%(2*binomial(n+2,3)) for n in range(1,81)] # G. C. Greubel, Apr 12 2024