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Product of numerator and denominator of the n-th harmonic number, 1 + 1/2 + 1/3 +...+ 1/n.
3

%I #14 May 01 2022 11:21:26

%S 1,6,66,300,8220,980,50820,213080,17965080,18600120,2320468920,

%T 2384502120,412970037480,422245703880,430902992520,1756076802480,

%U 516336630329520,58297387228080,21362271268818480,866533600973040,97555876321904,98772315738096,52866073370045936,481103506052529360

%N Product of numerator and denominator of the n-th harmonic number, 1 + 1/2 + 1/3 +...+ 1/n.

%C Numerator and denominator in definition have no common divisors >1.

%H Harvey P. Dale, <a href="/A064167/b064167.txt">Table of n, a(n) for n = 1..1000</a>

%e The 3rd harmonic number is 11/6. So a(3) = 11 * 6 = 66.

%t Numerator[#]Denominator[#]&/@HarmonicNumber[Range[30]] (* _Harvey P. Dale_, May 01 2022 *)

%o (PARI) a(n) = my(h=sum(k=1, n, 1/k)); numerator(h) * denominator(h); \\ _Michel Marcus_, Sep 07 2019

%Y Cf. A001008, A002805, A064168, A064169.

%K nonn

%O 1,2

%A _Leroy Quet_, Sep 19 2001

%E More terms from _Michel Marcus_, Sep 07 2019