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

2,1

Comments

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

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

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

Example

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.

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 *)

Crossrefs

Cf. A256966.

Sequence in context: A123753 A124288 A256966 * A330321 A205726 A002815

Adjacent sequences: A280941 A280942 A280943 * A280945 A280946 A280947

Keyword

nonn

Author

Jörg Zurkirchen, Jan 11 2017

Status

approved