A280944 Maximum sum of a set of different positive integers less than or equal to n whose pairwise sums are all different.

3, 6, 9, 13, 17, 21, 26, 31, 36, 41, 46, 52, 58, 64, 70, 76, 82, 88, 94, 101, 108, 115, 122, 129, 136, 144, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 248, 257, 266, 275, 284, 293, 302, 311, 320, 329, 339, 349, 359, 369, 379, 389, 399, 409, 419, 429, 439, 449, 459, 469, 479, 489, 499, 510, 521

Offset: 2

Author

Jörg Zurkirchen, Jan 11 2017

Keywords

• nonn

Comments

Only the terms a(2)..a(26) are identical to sequence A256966.

Values a(n) found by exhaustive search by a Rexx program.

Examples

			For n = 10, the optimum set of integers is {10, 9, 8, 6, 3} and thus a(10) = 36. The 10 pair sums {19, 18, 17, 16, 15, 14, 13, 12, 11, 9} are all different.
		

Links

• Jörg Zurkirchen, Table of n, a(n) for n = 2..240
• PuzzleUp, Problem No 06, Different sums, August 31, 2016.
• Jörg Zurkirchen, Table of optimum solutions for n = 2..240

Crossrefs

Cf. A256966.

Programs

Mathematica

Array[Max[Total /@ Select[Rest@ Subsets@ Range@ #, Length@ Union[Total /@ #] == Length[#] &@ Select[Union[Sort /@ Tuples[#, 2]], UnsameQ @@ # &] &]] &, 15, 2] (* Michael De Vlieger, Jan 21 2018 *)