A180491 Product of remainders of n mod k, for k = 2,3,4,...,n-1.

1, 1, 1, 0, 2, 0, 6, 0, 0, 0, 720, 0, 2160, 0, 0, 0, 2419200, 0, 65318400, 0, 0, 0, 754427520000, 0, 0, 0, 0, 0, 32953394073600000, 0, 311409573995520000, 0, 0, 0, 0, 0, 37269497815783833600000, 0, 0, 0, 7890485108998805913600000000, 0

Offset: 1

Author

Carl R. White, Sep 08 2010

Keywords

• nonn

Comments

a(n) is zero where n is composite and is trivially less than or equal to n! when n is prime or 1.

a(n)=0 iff n is composite. See A180492. - Robert G. Wilson v, Sep 09 2010

Examples

			a(7) = (7 mod 2) * (7 mod 3) * (7 mod 4) * (7 mod 5) * (7 mod 6) = 1 * 1 * 3 * 2 * 1 = 6.
		

Crossrefs

Cf. A034386, A000142, A004125, A180492, A180493.

Cf. A080339, A173392.

Programs

Maple

a:=proc(n) if n=1 then 1; elif isprime(n)=true then mul(n mod i, i=2..n-1); else 0; fi: end: seq(a(n), n=1..60); # Ridouane Oudra, Nov 01 2024

Mathematica

f[n_] := Times @@ Mod[n, Range[2, n - 1]]; Array[f, 42] (* Robert G. Wilson v, Sep 09 2010 *)

Formula

a(n) = A080339(n)*A173392(n). - Ridouane Oudra, Nov 01 2024