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%I #53 Nov 03 2019 12:05:41
%S 3,6,9,13,17,21,26,31,36,41,46,52,58,64,70,76,82,88,94,101,108,115,
%T 122,129,136,144,152,160,168,176,184,192,200,208,216,224,232,240,248,
%U 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
%N Maximum sum of a set of different positive integers less than or equal to n whose pairwise sums are all different.
%C Only the terms a(2)..a(26) are identical to sequence A256966.
%C Values a(n) found by exhaustive search by a Rexx program.
%H Jörg Zurkirchen, <a href="/A280944/b280944.txt">Table of n, a(n) for n = 2..240</a>
%H PuzzleUp, <a href="/A280944/a280944.png">Problem No 06, Different sums, August 31, 2016</a>.
%H Jörg Zurkirchen, <a href="/A280944/a280944_1.txt">Table of optimum solutions for n = 2..240</a>
%e 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.
%t 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 *)
%Y Cf. A256966.
%K nonn
%O 2,1
%A _Jörg Zurkirchen_, Jan 11 2017
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