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 A115855 #20 Dec 12 2024 15:17:50
%S A115855 0,1,3,6,12,21,35,58,106,188,243,493,593,1062,3275,5507,5803,12426,
%T A115855 12915,42410,131772,167587,168841,428012,839367,1015501,1968161,
%U A115855 5787286,5791850,15163758,15170599,28838712,75983559,82753547,486356262,1158442726,1158464362
%N A115855 Number of partitions of 1 into fractions i/j with 1<=i<j<=n and i,j coprime.
%F A115855 A115856(n) = a(n+1) - a(n).
%e A115855 a(4) = #{1/2+1/2, 1/2+1/4+1/4, 1/3+2/3, 1/3+1/3+1/3, 1/4+3/4, 1/4+1/4+1/4+1/4} = 6.
%t A115855 Table[Length@ Select[Flatten[Map[IntegerPartitions[1, {#}, Rest@ Union[Flatten@ TensorProduct[#, 1/#] &@ Range@ n /. {_Integer -> 0, k_ /; k > 1 -> 0}]] &, Range@ n], 1], Total@ # == 1 &], {n, 25}] (* _Michael De Vlieger_, Jul 15 2016 *) (* or *)
%t A115855 a[n_] := Sum[ Length@ IntegerPartitions[1, {k}, Union@ Flatten[ Table[i/j, {j, n}, {i, j-1}]]], {k, n}]; Array[a, 20] (* _Giovanni Resta_, Jun 15 2017 *)
%Y A115855 Cf. A000041, A002966, A038566, A038567, A115856, A116084.
%K A115855 nonn
%O A115855 1,3
%A A115855 _Reinhard Zumkeller_, Feb 01 2006
%E A115855 a(21)-a(28) from _Michael De Vlieger_, Jul 15 2016
%E A115855 More terms from _Jinyuan Wang_, Dec 11 2024