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A056612
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a(n) = gcd(n!, n!*(1 + 1/2 + 1/3 + ... + 1/n)).
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7
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1, 1, 1, 2, 2, 36, 36, 144, 144, 1440, 1440, 17280, 17280, 241920, 3628800, 29030400, 29030400, 1567641600, 1567641600, 156764160000, 9876142080000, 217275125760000, 217275125760000, 1738201006080000, 1738201006080000
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OFFSET
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1,4
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COMMENTS
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The first difference between this sequence and A131657 occurs for n = 20, while the first difference between this sequence and A131658 occurs for n = 21. - Christian Krattenthaler, Sep 30 2007
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LINKS
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FORMULA
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EXAMPLE
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a(4) = gcd(4!, 4!*(1 + 1/2 + 1/3 + 1/4)) = gcd(24, 50) = 2.
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MATHEMATICA
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Table[GCD[#, # Total@ Map[1/# &, Range@ n]] &[n!], {n, 25}] (* Michael De Vlieger, Sep 23 2017 *)
a[n_] := n!/Denominator@ HarmonicNumber@ n; Array[a, 25] (* Robert G. Wilson v, Jun 30 2018 *)
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PROG
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(PARI) a(n) = gcd(n!, n!*sum(k=1, n, 1/k)); \\ Michel Marcus, Jul 14 2018
(PARI) a(n) = gcd(stirling(n+1, 2, 1), n!); \\ Michel Marcus, May 20 2020
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CROSSREFS
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Cf. A334958 (similar sequence for the alternative harmonic series).
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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