Geometric triangles (noch nicht übersetzt)

Let us define a geometric triangle as an integer sided triangle with sides a ≤ b ≤ c so that its sides form a geometric progression, i.e. b² = a · c . 

An example of such a geometric triangle is the triangle with sides a = 144, b = 156 and c = 169.

There are 861805 geometric triangles with perimeter ≤ 10⁶ .

How many geometric triangles exist with perimeter ≤ 2.5·10¹³ ?