A232984 The Gauss factorial n_10!.

1, 1, 1, 3, 3, 3, 3, 21, 21, 189, 189, 2079, 2079, 27027, 27027, 27027, 27027, 459459, 459459, 8729721, 8729721, 183324141, 183324141, 4216455243, 4216455243, 4216455243, 4216455243, 113844291561, 113844291561, 3301484455269, 3301484455269, 102346018113339, 102346018113339, 3377418597740187

Offset: 0

Author

N. J. A. Sloane, Dec 08 2013

Keywords

• nonn

Comments

The Gauss factorial n_k! is defined to be Product_{1<=j<=n, gcd(j,k)=1} j.

Links

• J. B. Cosgrave and K. Dilcher, An introduction to Gauss factorials, Amer. Math. Monthly, 118 (2011), 810-828.
• J. B. Cosgrave and K. Dilcher, The Gauss-Wilson theorem for quarter-intervals, Acta Mathematica Hungarica, Sept. 2013.

Crossrefs

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.

Programs

Magma

k:=10; [IsZero(n) select 1 else &*[j: j in [1..n] | IsOne(GCD(j,k))]: n in [0..40]]; // Bruno Berselli, Dec 10 2013

Maple

Gf:=proc(N,n) local j,k; k:=1;
for j from 1 to N do if gcd(j,n)=1 then k:=j*k; fi; od; k; end;
f:=n->[seq(Gf(N,n),N=0..40)];
f(10);