A119690 n! mod n*(n+1)/2.

0, 2, 0, 4, 0, 6, 0, 0, 0, 10, 0, 12, 0, 0, 0, 16, 0, 18, 0, 0, 0, 22, 0, 0, 0, 0, 0, 28, 0, 30, 0, 0, 0, 0, 0, 36, 0, 0, 0, 40, 0, 42, 0, 0, 0, 46, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 58, 0, 60, 0, 0, 0, 0, 0, 66, 0, 0, 0, 70, 0, 72, 0, 0, 0, 0, 0, 78, 0, 0, 0, 82, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Jun 09 2006

Keywords

• easy
• nonn

Comments

All terms are even.

It appears that f(n)=(n!)^(2k+1) modulo n(n+1)/2 is n if n is one less than an odd prime, else f(n) is 0, for any integer k. See A175567 for related results involving an even power of n!. - John W. Layman, Jul 12 2010

Crossrefs

Cf. A006093, A010051, A175567, A175553.

Programs

Magma

[ Factorial(n) mod (n*(n+1) div 2): n in [1..100] ];

Maple

P:=proc(n) local i, j, k; j:=1; k:=0; for i from 1 by 1 to n do j:=j*i; k:=k+i; print(j mod k); od; end: P(100);

Formula

a(n) = n if n+1 is an odd prime, a(n) = 0 otherwise.