Areas of the triangles given in S000996.
6, 12, 12, 30, 60, 24, 84, 36, 60, 120, 66, 42, 84, 126, 60, 90, 84, 168, 36, 204, 210, 210, 60, 120, 132, 72, 84, 252, 360, 114, 156, 180, 210, 420, 120, 210, 420, 168, 420, 240, 468, 126, 180, 336, 360, 420, 264, 330, 252, 168, 504, 420, 780, 420, 306, 456
1
All these areas are a multiple of 6. This sequence is the same as A072294. Sequence S000999 gives the union of all terms in this sequence; that is, each number appears only once and the numbers are sorted.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
(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, ar]]], {a, nn}, {b, a}, {c, b}]; t
Cf. A072294, S000996, S000999.
nonn
T. D. Noe, Apr 10 2017, modified Apr 13 2017