A308222 Numbers that are the perimeter of a primitive Heronian isosceles triangle.

16, 18, 36, 50, 64, 98, 100, 144, 162, 196, 242, 256, 324, 338, 400, 450, 484, 576, 578, 676, 722, 784, 882, 900, 1024, 1058, 1156, 1250, 1296, 1444, 1458, 1600, 1682, 1764, 1922, 1936, 2116, 2178, 2304, 2450, 2500, 2704, 2738, 2916, 3042, 3136

Offset: 1

Author

Peter Kagey, May 16 2019

Keywords

• nonn

Comments

A primitive Heronian triangle is a triangle with integer sides and area, where the side lengths do not share a common divisor.

Examples

			Table illustrating first six terms of the sequence:
  perimeter |   sides    | area
  ----------+------------+-----
      16    |  (5,5,6)   |  12
      18    |  (5,5,8)   |  12
      36    | (10,13,13) |  60
      50    | (13,13,24) |  60
      50    | (16,17,17) | 120
      64    | (14,25,25) | 168
      64    | (17,17,30) | 120
      98    | (24,37,37) | 420
      98    | (25,25,48) | 168
      98    | (29,29,40) | 420
		

Links

• Mathematics Stack Exchange user "George", Semiperimeter of isosceles Heronian triangles.
• Wikipedia, Isosceles Heronian triangles.

Crossrefs

Cf. A046790, A096033, A096468.

Formula

a(n) = 2*A096033(n+2) (conjectured).