A286015 Sum of largest parts of all partitions of n into consecutive parts.

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, 34, 58, 35, 44, 58, 47, 32, 70, 44, 70, 57, 56, 49, 82, 50, 62, 78, 65, 53, 114, 59, 71, 65, 84, 76, 106, 62, 80, 98, 106, 67, 118, 74, 89, 106, 92, 79, 153, 64, 124

Offset: 1

Author

Omar E. Pol, Apr 30 2017

Keywords

• nonn

Comments

If n is a power of 2 then a(n) = n, the same as A286014(n).

Conjecture: this is also the row sums of A286013.

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000079, A006128, A046746, A204217, A211343, A245579, A286013, A286014.

Programs

Mathematica

Table[Total[Select[IntegerPartitions@ n, Or[Length@ # == 1, Union@ Differences@ # == {-1}] &][[All, 1]]], {n, 65}] (* Michael De Vlieger, Jul 21 2017 *)

Extensions

More terms from Alois P. Heinz, May 01 2017