|
%I #14 Feb 24 2022 02:06:18
%S 1,1,1,1,1,5,5,35,35,35,35,385,385,5005,5005,5005,5005,85085,85085,
%T 1616615,1616615,1616615,1616615,37182145,37182145,929553625,
%U 929553625,929553625,929553625,26957055125,26957055125,835668708875,835668708875,835668708875,835668708875,29248404810625,29248404810625
%N The Gauss factorial n_6!.
%C The Gauss factorial n_k! is defined to be Product_{1<=j<=n, gcd(j,k)=1} j.
%H J. B. Cosgrave and K. Dilcher, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.118.09.812">An introduction to Gauss factorials</a>, Amer. Math. Monthly, 118 (2011), 810-828.
%H J. B. Cosgrave and K. Dilcher, <a href="http://dx.doi.org/10.1007/s10474-013-0357-1">The Gauss-Wilson theorem for quarter-intervals</a>, Acta Mathematica Hungarica, Sept. 2013.
%p Gf:=proc(N,n) local j,k; k:=1;
%p for j from 1 to N do if gcd(j,n)=1 then k:=j*k; fi; od; k; end;
%p f:=n->[seq(Gf(N,n),N=0..40)];
%p f(6);
%o (Magma) k:=6; [IsZero(n) select 1 else &*[j: j in [1..n] | IsOne(GCD(j,k))]: n in [0..40]]; // _Bruno Berselli_, Dec 10 2013
%Y The Gauss factorials n_1!, n_2!, n_3!, n_5!, n_6!, n_7!, n_10!, n_11! are A000142, A055634, A232980-A232985 respectively.
%K nonn
%O 0,6
%A _N. J. A. Sloane_, Dec 08 2013
|
