|
| |
|
|
A232982
|
|
The Gauss factorial n_6!.
|
|
1
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
| |
|
|
