A124441 - OEIS

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

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OFFSET

1,5

COMMENTS

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

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)

FORMULA

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

EXAMPLE

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.

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 *)

PROG

(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

CROSSREFS

Cf. A124442, A001783.

Sequence in context: A062566 A126265 A293182 * A284475 A353660 A285355

Adjacent sequences: A124438 A124439 A124440 * A124442 A124443 A124444