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A232980
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The Gauss factorial n_3!.
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7
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1, 1, 2, 2, 8, 40, 40, 280, 2240, 2240, 22400, 246400, 246400, 3203200, 44844800, 44844800, 717516800, 12197785600, 12197785600, 231757926400, 4635158528000, 4635158528000, 101973487616000, 2345390215168000, 2345390215168000, 58634755379200000, 1524503639859200000, 1524503639859200000
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OFFSET
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0,3
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COMMENTS
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The Gauss factorial n_k! is defined to be Product_{1<=j<=n, gcd(j,k)=1} j.
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LINKS
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Table of n, a(n) for n=0..27.
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.
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MAPLE
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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(3);
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PROG
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(Magma) k:=3; [IsZero(n) select 1 else &*[j: j in [1..n] | IsOne(GCD(j, k))]: n in [0..30]]; // Bruno Berselli, Dec 10 2013
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CROSSREFS
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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: A102647 A318869 A060224 * A212307 A111605 A009544
Adjacent sequences: A232977 A232978 A232979 * A232981 A232982 A232983
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Dec 08 2013
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STATUS
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approved
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