--description--

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. $b^2 = a \times c$.

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

There are $861\,805$ geometric triangles with $\text{perimeter} ≤ {10}^6$.

How many geometric triangles exist with $\text{perimeter} ≤ 2.5 \times {10}^{13}$?

--hints--

geometricTriangles() should return 41791929448408.

assert.strictEqual(geometricTriangles(), 41791929448408);

--seed--

--seed-contents--

function geometricTriangles() {

  return true;
}

geometricTriangles();

--solutions--

// solution required