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A055592 Longest side of congruent triangles with integer sides and positive integer area, ordered by longest side, then second longest side and finally shortest side.

%I A055592 #13 Jul 30 2017 15:36:04
%S A055592 5,6,8,10,12,13,13,15,15,15,16,17,17,17,18,20,20,20,21,21,24,24,24,25,
%T A055592 25,25,25,26,26,26,26,28,29,29,30,30,30,30,30,30,30,32,34,34,34,35,35,
%U A055592 35,36,36,37,37,37,37,37,39,39,39,39,39,39,40,40,40,40,40,40,40,41,41
%N A055592 Longest side of congruent triangles with integer sides and positive integer area, ordered by longest side, then second longest side and finally shortest side.
%H A055592 Ray Chandler, <a href="/A055592/b055592.txt">Table of n, a(n) for n = 1..10000</a>
%t A055592 max = 41; triangles = Reap[Do[s = (a+b+c)/2; area = Sqrt[s*(s-a)*(s-b)*(s-c)]; If[IntegerQ[area] && area > 0, Sow[{a, b, c, area}]], {a, 1, max}, {b, a, max}, {c, b, max}]][[2, 1]]; A055592 = Sort[triangles, #1[[3]]*max^2 + #1[[2]]*max + #1[[1]] < #2[[3]]* max^2 + #2[[2]]*max + #2[[1]] &][[All, 3]](* _Jean-François Alcover_, Jun 12 2012 *)
%Y A055592 Cf. A055593, A055594, A055595.
%K A055592 nonn
%O A055592 1,1
%A A055592 _Henry Bottomley_, May 26 2000