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A058067
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Number of polynomial functions from Z to Z/nZ.
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3
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1, 1, 4, 27, 64, 3125, 108, 823543, 1024, 19683, 12500, 285311670611, 1728, 302875106592253, 3294172, 84375, 65536, 827240261886336764177, 78732, 1978419655660313589123979, 200000, 22235661, 1141246682444, 20880467999847912034355032910567
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OFFSET
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0,3
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COMMENTS
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The first formula for a(n) is due to Kempner (1921). - Jonathan Sondow, Nov 05 2017
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LINKS
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FORMULA
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a(n) = Product_{k=0..n-1} n/gcd(n, k!).
Multiplicative with a(p^e) = p^t_p(e). - David W. Wilson, Aug 14 2005 [t_p(e) = Sum_{k>=0: e > A090622(k, p)} (e - A090622(k, p)) = p * Sum_{k = 1..e} max(0, k - A090622(e-k, p)). In particular, t_p(e) = p*e*(e+1)/2 for e <= p. - Andrey Zabolotskiy, Nov 09 2017 and Sep 29 2020]
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MAPLE
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A058067 := n->mul(n/gcd(n, k!), k=0..n-1);
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MATHEMATICA
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a[0] = 1; a[n_] := Product[n/GCD[n, k!], {k, 0, n - 1}]; Array[a, 24, 0] (* Amiram Eldar, Sep 29 2020 *)
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PROG
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(PARI) a(n) = prod(k=0, n-1, n/gcd(n, k!)); \\ Michel Marcus, Nov 06 2017
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CROSSREFS
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KEYWORD
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nonn,mult,easy
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AUTHOR
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STATUS
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approved
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