A305888 Numbers that are the perimeter of a Heronian triangle, but not of a primitive Heronian triangle.

24, 88, 280, 472, 558, 664, 696, 852, 856, 1048, 1432, 1720, 1816, 2008, 2180, 2292, 2680, 2776, 2868, 3144, 3352, 3544, 3576, 3582, 3732, 3736, 3860, 3928, 4192, 4308, 4504, 4696, 4878, 4976, 5080, 5172, 5272, 5464, 5598, 5748, 6520, 6616, 6740, 6744, 7188

Offset: 1

Author

Giovanni Resta, Jun 14 2018

Keywords

• nonn

Comments

Numbers in A051518 that are not in A096468.

Examples

			The only Heronian triangle with perimeter 24 has sides {6, 8, 10} and thus it is not primitive. Hence 24 is in the sequence.
		

Links

• Eric Weisstein's World of Mathematics, Heronian Triangle

Crossrefs

Cf. A051518, A096468.

Programs

Mathematica

hpp[p_] := Catch@Block[{t=0, c, q=p/2}, Do[c = p-a-b; If[c >= b && a+c > b && a+b > c && IntegerQ@ Sqrt[q (q-a) (q-b) (q-c)], t++; If[GCD[a, b, c] == 1, Throw@ False]], {a, p/3}, {b, a, p-a-1}]; t > 0]; Select[2 Range[350], hpp]