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%I #37 May 23 2020 02:18:16
%S 1,1,1,2,2,36,36,144,144,1440,1440,17280,17280,241920,3628800,
%T 29030400,29030400,1567641600,1567641600,156764160000,9876142080000,
%U 217275125760000,217275125760000,1738201006080000,1738201006080000
%N a(n) = gcd(n!, n!*(1 + 1/2 + 1/3 + ... + 1/n)).
%C 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
%H Michael De Vlieger, <a href="/A056612/b056612.txt">Table of n, a(n) for n = 1..535</a>
%F a(n) = A000142(n)/A002805(n) = A000254(n)/A001008(n). - _Franz Vrabec_, Sep 13 2005
%F a(n) = gcd(A000254(n+1), A000254(n)). - _Petros Hadjicostas_, May 18 2020
%F a(n) = gcd(Stirling1(n+1, 2), n!). - _Michel Marcus_, May 20 2020
%e a(4) = gcd(4!, 4!*(1 + 1/2 + 1/3 + 1/4)) = gcd(24, 50) = 2.
%e 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
%t Table[GCD[#, # Total@ Map[1/# &, Range@ n]] &[n!], {n, 25}] (* _Michael De Vlieger_, Sep 23 2017 *)
%t a[n_] := n!/Denominator@ HarmonicNumber@ n; Array[a, 25] (* _Robert G. Wilson v_, Jun 30 2018 *)
%o (PARI) a(n) = gcd(n!, n!*sum(k=1, n, 1/k)); \\ _Michel Marcus_, Jul 14 2018
%o (PARI) a(n) = gcd(stirling(n+1, 2, 1), n!); \\ _Michel Marcus_, May 20 2020
%Y Cf. A000142, A001008, A002805.
%Y Cf. A007757, A131657, A131658.
%Y Cf. A334958 (similar sequence for the alternative harmonic series).
%K easy,nonn
%O 1,4
%A _Leroy Quet_, Aug 08 2000
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