A232982 The Gauss factorial n_6!.

1, 1, 1, 1, 1, 5, 5, 35, 35, 35, 35, 385, 385, 5005, 5005, 5005, 5005, 85085, 85085, 1616615, 1616615, 1616615, 1616615, 37182145, 37182145, 929553625, 929553625, 929553625, 929553625, 26957055125, 26957055125, 835668708875, 835668708875, 835668708875, 835668708875, 29248404810625, 29248404810625

Offset

0,6

Comments

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

Links

Table of n, a(n) for n=0..36.

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.

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(6);

Prog

(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

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.

Sequence in context: A208950 A160672 A355952 * A160555 A067047 A271054

Adjacent sequences: A232979 A232980 A232981 * A232983 A232984 A232985

Keyword

nonn

Author

N. J. A. Sloane, Dec 08 2013

Status

approved