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A119619
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a(n) = Product_{i=1..n} i / gcd(i,n).
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4
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1, 1, 2, 3, 24, 10, 720, 315, 4480, 4536, 3628800, 11550, 479001600, 13899600, 43051008, 638512875, 20922789888000, 1905904000, 6402373705728000, 118794043368, 68108451840000, 4535772564960000, 1124000727777607680000
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = Product_{d|n} pxi(d), where pxi(m) = is the product of totatives of m (A001783). - Jaroslav Krizek, Dec 28 2016
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MAPLE
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a:=n->mul(numer (k/n), k=1..n): seq(a(n), n=1..23); # Zerinvary Lajos, Apr 26 2008
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MATHEMATICA
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a[n_] := Product[i/GCD[i, n], {i, 1, n}]; Table[a[n], {n, 1, 30}] (* Stefan Steinerberger, Jun 08 2006 *)
Table[Product[Times @@ Select[Range@ d, CoprimeQ[#, d] &], {d, Divisors@ n}], {n, 23}] (* Michael De Vlieger, Dec 28 2016 *)
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PROG
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(PARI) a(n) = prod(i=1, n, i/gcd(i, n))
(Magma) [&*[&*[h: h in [1..d] | GCD(h, d) eq 1]: d in Divisors(n)]: n in [1..100]]; // Jaroslav Krizek, Dec 28 2016
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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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