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 A286015 #21 Jul 21 2017 12:11:34
%S A286015 1,2,5,4,8,9,11,8,18,14,17,17,20,19,34,16,26,31,29,26,46,29,35,33,45,
%T A286015 34,58,35,44,58,47,32,70,44,70,57,56,49,82,50,62,78,65,53,114,59,71,
%U A286015 65,84,76,106,62,80,98,106,67,118,74,89,106,92,79,153,64,124
%N A286015 Sum of largest parts of all partitions of n into consecutive parts.
%C A286015 If n is a power of 2 then a(n) = n, the same as A286014(n).
%C A286015 Conjecture: this is also the row sums of A286013.
%H A286015 Alois P. Heinz, <a href="/A286015/b286015.txt">Table of n, a(n) for n = 1..10000</a>
%e A286015 For n = 15 there are four partitions of 15 into consecutive parts: [15], [8, 7], [6, 5, 4] and [5, 4, 3, 2, 1]. The sum of the largest parts is 15 + 8 + 6 + 5 = 34, so a(15) = 34.
%t A286015 Table[Total[Select[IntegerPartitions@ n, Or[Length@ # == 1, Union@ Differences@ # == {-1}] &][[All, 1]]], {n, 65}] (* _Michael De Vlieger_, Jul 21 2017 *)
%Y A286015 Cf. A000079, A006128, A046746, A204217, A211343, A245579, A286013, A286014.
%K A286015 nonn
%O A286015 1,2
%A A286015 _Omar E. Pol_, Apr 30 2017
%E A286015 More terms from _Alois P. Heinz_, May 01 2017