A112287 a(n) = denominator of sum of reciprocals of the terms of the continued fraction for H(n) = Sum_{k=1..n} 1/k.

1, 2, 5, 12, 24, 4, 5, 35, 420, 156, 300, 45, 15, 39, 15351, 72, 1848, 10675, 300, 2142, 36, 5460, 15, 1870, 90, 63, 2040, 120, 138600, 3960, 1750320, 1324895, 440, 3945480, 5220, 158340, 1680, 3341100, 498960, 48048, 1260, 69264, 1510, 1168200, 568260

Offset: 1

Author

Leroy Quet, Sep 01 2005

Keywords

• nonn
• frac

Examples

			1 +1/2 +1/3 +1/4 +1/5 +1/6 = 49/20 = 2 + 1/(2 + 1/(4 + 1/2)).
So a(6) is 4, the denominator of 7/4 = 1/2 + 1/2 + 1/4 + 1/2.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Harmonic Number
• Eric Weisstein's World of Mathematics, Continued Fraction

Crossrefs

m-th harmonic number H(m) = A001008(m)/A002805(m).

Cf. A055573, A058027, A100398, A110020, A112286.

Programs

Mathematica

f[n_] := Plus @@ (1/# &) /@ ContinuedFraction[Sum[1/k, {k, n}]]; Table[Denominator[f[n]], {n, 45}] (* Ray Chandler, Sep 06 2005 *)

Extensions

Extended by Hans Havermann and Ray Chandler, Sep 06 2005