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%I #28 Nov 01 2019 09:36:14
%S 1,1,2,3,12,5,120,35,280,63,30240,77,665280,1287,16016,19305,
%T 518918400,2431,17643225600,46189,14780480,1322685,28158588057600,
%U 96577,4317650168832,58503375,475931456000,75218625,3497296636753920000,215441,202843204931727360000
%N a(n) = Product_{ceiling(n/2) <= k <= n, gcd(k,n)=1} k.
%H Alois P. Heinz, <a href="/A124442/b124442.txt">Table of n, a(n) for n = 1..300</a>
%H J. B. Cosgrave, K. Dilcher, <a href="http://www.emis.de/journals/INTEGERS/papers/i39/i39.Abstract.html"> Extensions of the Gauss-Wilson Theorem</a>, Integers: Electronic Journal of Combinatorial Number Theory, 8(2008)
%F a(n) = A001783(n)/A124441(n). - _M. F. Hasler_, Jul 23 2011
%e The integers which are >= 9/2 and are <= 9 and which are coprime to 9 are 5, 7 and 8. So a(9) = 5*7*8 = 280.
%p a:=proc(n) local b,k: b:=1: for k from ceil(n/2) to n do if gcd(k,n)=1 then b:=b*k else b:=b fi od: b; end: seq(a(n),n=1..33); # _Emeric Deutsch_, Nov 03 2006
%t f[n_] := Times @@ Select[Range[Ceiling[n/2], n], GCD[ #, n] == 1 &];Table[f[n], {n, 30}] (* _Ray Chandler_, Nov 12 2006 *)
%o (PARI) A124442(n)=prod(k=(n+1)\2,n-1, k^(gcd(k, n)==1)) \\ _M. F. Hasler_, Jul 23 2011
%o (Sage)
%o def Gauss_factorial(N, n): return mul(j for j in (1..N) if gcd(j, n) == 1)
%o def A124442(n): return Gauss_factorial(n, n)/Gauss_factorial(n//2, n)
%o [A124442(n) for n in (1..29)] # _Peter Luschny_, Oct 01 2012
%Y Cf. A124441.
%K nonn
%O 1,3
%A _Leroy Quet_, Nov 01 2006
%E More terms from _Emeric Deutsch_, Nov 03 2006
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