Triples x <= y <= z (sorted by z, y,and x) that form the sides of a primitive triangle having integer area.

3, 4, 5, 5, 5, 6, 5, 5, 8, 5, 12, 13, 10, 13, 13, 4, 13, 15, 13, 14, 15, 9, 10, 17, 8, 15, 17, 16, 17, 17, 11, 13, 20, 7, 15, 20, 10, 17, 21, 13, 20, 21, 13, 13, 24, 12, 17, 25, 7, 24, 25, 14, 25, 25, 3, 25, 26, 17, 25, 26, 17, 25, 28, 20, 21, 29, 6, 25, 29

1

Note that the sides are in reverse order in S000996.

T. D. Noe, Plot of 1000 triples

T. D. Noe, Table of 1000 triples

(Mma) area[a_Integer, b_Integer, c_Integer] := Sqrt[(a + b + c) (-a + b + c) (a - b + c) (a + b - c)] / 4; nn = 50; t = {}; Do[If[GCD[a, b, c] == 1 && a < b + c, ar = area[a, b, c]; If[IntegerQ[ar], AppendTo[t, {c, b, a}]]], {a, nn}, {b, a}, {c, b}]; t

Cf. S000996.

nonn,tabl

T. D. Noe, Apr 10 2017