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 A154886 #18 Jun 14 2018 02:23:13
%S A154886 1,5,51,655,20980,578779,46097340,2889706132,485416306983,
%T A154886 68334145684271,24330218582223815,3847311627258606534,
%U A154886 2716890193805515507433,1270766589764097820833691,2188031110546839992589840986,1331298554328475793875243619997
%N A154886 Number of ways to partition n into reduced fractions i/j with j <= n.
%H A154886 Robert Gerbicz, <a href="/A154886/b154886.txt">Table of n, a(n) for n = 1..43</a>
%e A154886 a(2) = #{2, 3/2+1/2, 1+1, 1+1/2+1/2, 1/2+1/2+1/2+1/2} = 5.
%t A154886 modifiedFarey[n_] := Union@ Flatten@ Table[a/b, {b, n}, {a, b*n}]; t[n_, k_] := Length@ IntegerPartitions[n, {k}, modifiedFarey@ n]; Plus @@@ Table[t[n, k], {n, 7, 7}, {k, n*(Plus @@ EulerPhi@ Range@n)}] (* _Robert G. Wilson v_, Aug 30 2010 *)
%Y A154886 Cf. A154887, A119983, A143270.
%K A154886 nonn
%O A154886 1,2
%A A154886 _Reinhard Zumkeller_, Jan 17 2009
%E A154886 a(7) from _Robert G. Wilson v_, Aug 30 2010
%E A154886 a(8)-a(16) from _Robert Gerbicz_, Nov 19 2010