

A280944


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


1



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
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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 * A205726 A002815 A109512
Adjacent sequences: A280941 A280942 A280943 * A280945 A280946 A280947


KEYWORD

nonn


AUTHOR

Jörg Zurkirchen, Jan 11 2017


STATUS

approved



