This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A112287 #13 Feb 16 2025 08:32:59
%S A112287 1,2,5,12,24,4,5,35,420,156,300,45,15,39,15351,72,1848,10675,300,2142,
%T A112287 36,5460,15,1870,90,63,2040,120,138600,3960,1750320,1324895,440,
%U A112287 3945480,5220,158340,1680,3341100,498960,48048,1260,69264,1510,1168200,568260
%N A112287 a(n) = denominator of sum of reciprocals of the terms of the continued fraction for H(n) = Sum_{k=1..n} 1/k.
%H A112287 G. C. Greubel, <a href="/A112287/b112287.txt">Table of n, a(n) for n = 1..1000</a>
%H A112287 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a>
%H A112287 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ContinuedFraction.html">Continued Fraction</a>
%e A112287 1 +1/2 +1/3 +1/4 +1/5 +1/6 = 49/20 = 2 + 1/(2 + 1/(4 + 1/2)).
%e A112287 So a(6) is 4, the denominator of 7/4 = 1/2 + 1/2 + 1/4 + 1/2.
%t A112287 f[n_] := Plus @@ (1/# &) /@ ContinuedFraction[Sum[1/k, {k, n}]]; Table[Denominator[f[n]], {n, 45}] (* _Ray Chandler_, Sep 06 2005 *)
%Y A112287 m-th harmonic number H(m) = A001008(m)/A002805(m).
%Y A112287 Cf. A055573, A058027, A100398, A110020, A112286.
%K A112287 nonn,frac
%O A112287 1,2
%A A112287 _Leroy Quet_, Sep 01 2005
%E A112287 Extended by _Hans Havermann_ and _Ray Chandler_, Sep 06 2005