A334983 Perimeters of Heronian triangles where the lengths of the smallest and largest sides are coprime.

12, 16, 18, 30, 32, 36, 40, 42, 44, 48, 50, 54, 56, 60, 64, 66, 68, 70, 72, 76, 78, 80, 84, 90, 96, 98, 100, 104, 108, 110, 112, 114, 120, 126, 128, 130, 132, 140, 144, 150, 152, 154, 156, 160, 162, 164, 168, 170, 172, 174, 176, 180, 182, 186, 190, 192, 196, 198, 200, 204

Offset: 1

Author

Wesley Ivan Hurt, May 18 2020

Keywords

• nonn

Comments

This sequence includes the perimeters of all primitive Heronian triangles (A096468). First differs from A096468 at a(38) = 140.

Examples

			a(1) = 12; there is one Heronian triangle with perimeter 12, which is [3,4,5] and the lengths of the smallest and largest sides are coprime (GCD(3,5) = 1).
a(5) = 32; there is one Heronian triangle with perimeter 32, [4,13,15] and the lengths of the smallest and middle sides are coprime (GCD(4,13) = 1).
		

Links

• Eric Weisstein's World of Mathematics, Heronian Triangle
• Wikipedia, Heronian triangle
• Wikipedia, Integer Triangle

Crossrefs

Cf. A051518, A096468, A334984, A334989.