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

1,1

Comments

Numbers in A051518 that are not in A096468.

Links

Table of n, a(n) for n=1..45.

Eric Weisstein's World of Mathematics, Heronian Triangle

Example

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

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]

Crossrefs

Cf. A051518, A096468.

Sequence in context: A044211 A044592 A211632 * A233644 A010012 A256718

Adjacent sequences: A305885 A305886 A305887 * A305889 A305890 A305891

Keyword

nonn

Author

Giovanni Resta, Jun 14 2018

Status

approved