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 A119983 #13 Dec 12 2024 10:05:45
%S A119983 1,2,4,7,13,22,36,59,107,189,244,494,594,1063,3276,5508,5804,12427,
%T A119983 12916,42411,131773,167588,168842,428013,839368,1015502,1968162,
%U A119983 5787287,5791851,15163759,15170600,28838713,75983560,82753548,486356263,1158442727,1158464363
%N A119983 Number of ways to partition 1 into reduced fractions i/j with j <= n.
%C A119983 The reduced fractions are the Farey fractions of order n (A005728). - _Robert G. Wilson v_, Aug 30 2010
%F A119983 For p prime, a(p) = a(p-1) + P(p) - 1, where P is the partition function (A000041).
%e A119983 a(3) = 4; 1 = 1/1 = 1/2 + 1/2 = 2/3 + 1/3 = 1/3 + 1/3 + 1/3.
%t A119983 Farey[n_] := Union@ Flatten@ Table[a/b, {b, n}, {a, b}]; f[n_] := Length@ IntegerPartitions[1, All, Farey@ n]; Array[f, 27] (* _Robert G. Wilson v_, Aug 30 2010 *)
%Y A119983 Cf. A000041, A020473, A115855 (one less), A115856.
%Y A119983 Cf. A154886, A154888. - _Reinhard Zumkeller_, Jan 17 2009
%K A119983 nonn
%O A119983 1,2
%A A119983 _Franklin T. Adams-Watters_, Aug 01 2006
%E A119983 Definition corrected by _Reinhard Zumkeller_, Jan 17 2009
%E A119983 a(21)-a(27) from _Robert G. Wilson v_, Aug 30 2010
%E A119983 More terms from _Jinyuan Wang_, Dec 12 2024