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A124442
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a(n) = Product_{ceiling(n/2) <= k <= n, gcd(k,n)=1} k.
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4
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1, 1, 2, 3, 12, 5, 120, 35, 280, 63, 30240, 77, 665280, 1287, 16016, 19305, 518918400, 2431, 17643225600, 46189, 14780480, 1322685, 28158588057600, 96577, 4317650168832, 58503375, 475931456000, 75218625, 3497296636753920000, 215441, 202843204931727360000
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OFFSET
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1,3
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LINKS
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FORMULA
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EXAMPLE
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The integers which are >= 9/2 and are <= 9 and which are coprime to 9 are 5, 7 and 8. So a(9) = 5*7*8 = 280.
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MAPLE
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a:=proc(n) local b, k: b:=1: for k from ceil(n/2) to n do if gcd(k, n)=1 then b:=b*k else b:=b fi od: b; end: seq(a(n), n=1..33); # Emeric Deutsch, Nov 03 2006
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MATHEMATICA
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f[n_] := Times @@ Select[Range[Ceiling[n/2], n], GCD[ #, n] == 1 &]; Table[f[n], {n, 30}] (* Ray Chandler, Nov 12 2006 *)
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PROG
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(Sage)
def Gauss_factorial(N, n): return mul(j for j in (1..N) if gcd(j, n) == 1)
def A124442(n): return Gauss_factorial(n, n)/Gauss_factorial(n//2, n)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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