A124441 a(n) = Product_{1<=k<=n/2, gcd(k,n)=1} k.

1, 1, 1, 1, 2, 1, 6, 3, 8, 3, 120, 5, 720, 15, 56, 105, 40320, 35, 362880, 189, 3200, 945, 39916800, 385, 9580032, 10395, 3203200, 19305, 87178291200, 1001, 1307674368000, 2027025, 65228800, 2027025, 4839284736, 85085, 6402373705728000, 34459425, 17827532800

Offset: 1

Author

Leroy Quet, Nov 01 2006

Keywords

• nonn

Comments

a(n) divides A001783(n). - M. F. Hasler, Jul 23 2011

Examples

			The positive integers which are <= 9/2 and which are coprime to 9 are 1, 2 and 4. So a(9) = 1*2*4 = 8.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..800
• J. B. Cosgrave and K. Dilcher, Extensions of the Gauss-Wilson Theorem, Integers: Electronic Journal of Combinatorial Number Theory, 8 (2008)

Crossrefs

Cf. A124442, A001783.

Programs

Maple

a:=proc(n) local b,k: b:=1: for k from 1 to floor(n/2) do if gcd(k,n)=1 then b:=b*k else b:=b fi od: b; end: seq(a(n),n=1..41); # Emeric Deutsch, Nov 03 2006

Mathematica

f[n_] := Times @@ Select[Range[Floor[n/2]], GCD[ #, n] == 1 &];Table[f[n], {n, 36}] (* Ray Chandler, Nov 12 2006 *)

PARI

A124441(n)=prod(k=2, n\2, k^(gcd(k, n)==1))  \\  M. F. Hasler, Jul 23 2011

Sage

def Gauss_factorial(N, n): return mul(j for j in (1..N) if gcd(j, n) == 1)
def A124441(n): return Gauss_factorial(n//2, n)
[A124441(n) for n in (1..36)] # Peter Luschny, Oct 01 2012

Formula

a(n) = A001783(n)/A124442(n). - M. F. Hasler, Jul 23 2011

Extensions

More terms from Emeric Deutsch, Nov 03 2006