## S000999

Integer areas of the primitive triangles having integer sides.

6, 12, 24, 30, 36, 42, 60, 66, 72, 84, 90, 114, 120, 126, 132, 156, 168, 180, 198, 204, 210, 216, 234, 240, 252, 264, 270, 288, 300, 306, 330, 336, 360, 390, 396, 408, 420, 456, 462, 468, 480, 504, 510, 522, 528, 546, 570, 624, 630, 660, 684, 690, 714, 720, 744

1

These are the areas of the triangles which appear in S000996 and S000997. It is the union of all areas appearing in S000998. This sequence is very similar to A226453 but without the requirement that a side be prime.

T. D. Noe, Plot of 485 terms (those less than 10000)

T. D. Noe, Table of 485 terms (those less than 10000)

(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}]; Select[Union[t], # < Sqrt[2] * nn&]

Cf. A226453, S000996S000997, S000998.

nonn,hard

T. D. Noe, Apr 13 2017