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A056612
a(n) = gcd(n!, n!*(1 + 1/2 + 1/3 + ... + 1/n)).
7
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
OFFSET
1,4
COMMENTS
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
LINKS
FORMULA
a(n) = A000142(n)/A002805(n) = A000254(n)/A001008(n). - Franz Vrabec, Sep 13 2005
a(n) = gcd(A000254(n+1), A000254(n)). - Petros Hadjicostas, May 18 2020
a(n) = gcd(Stirling1(n+1, 2), n!). - Michel Marcus, May 20 2020
EXAMPLE
a(4) = gcd(4!, 4!*(1 + 1/2 + 1/3 + 1/4)) = gcd(24, 50) = 2.
a(4) = gcd(A000254(5), A000254(4)) = gcd(5!*(1 + 1/2 + 1/3 + 1/4 + 1/5), 4!*(1 + 1/2 + 1/3 + 1/4)) = gcd(274, 50) = 2. - Petros Hadjicostas, May 18 2020
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Cf. A334958 (similar sequence for the alternative harmonic series).
Sequence in context: A334470 A286375 A367091 * A131658 A131657 A298993
KEYWORD
easy,nonn
AUTHOR
Leroy Quet, Aug 08 2000
STATUS
approved