A072230 a(n) = n! (mod n^2), that is, n factorial modulo n^2.

0, 2, 6, 8, 20, 0, 42, 0, 0, 0, 110, 0, 156, 0, 0, 0, 272, 0, 342, 0, 0, 0, 506, 0, 0, 0, 0, 0, 812, 0, 930, 0, 0, 0, 0, 0, 1332, 0, 0, 0, 1640, 0, 1806, 0, 0, 0, 2162, 0, 0, 0, 0, 0, 2756, 0, 0, 0, 0, 0, 3422, 0, 3660, 0, 0, 0, 0, 0, 4422, 0, 0, 0, 4970, 0, 5256, 0, 0, 0, 0, 0, 6162

Offset: 1

Author

Roman Stawski, Jul 05 2002

Keywords

• nonn
• easy

Comments

With the exception of n=4, if n is composite, a(n) = 0. If n is prime, a(n) = n*(n-1). For example, a(11) = 11*10 = 110, a(41) = 41*40 = 1640. - Gary Detlefs, May 01 2010

Crossrefs

Cf. A002378, A008837.

Programs

Mathematica

Table[Mod[n!, n^2], {n, 79}] (* or *)
Table[Which[n == 4, Mod[n!, n^2], PrimeQ@ n, n (n - 1), True, 0], {n, 79}] (* Michael De Vlieger, Oct 14 2016 *)

PARI

a(n)=if(isprime(n), n*(n-1), if(n==4, 8, 0)) \\ Charles R Greathouse IV, Dec 14 2015

Formula

a(n) = A174530(n)*(A174530(n)-1) for n>=5. - Filip Zaludek, Oct 13 2016