Consider the right-angled triangle with sides $a=7$, $b=24$ and $c=25$.
The area of this triangle is 84, which is divisible by the perfect numbers 6 and 28.
Moreover it is a primitive right-angled triangle as $gcd(a,b) = 1$ and $gcd(b,c) = 1$.
Also $c$ is a perfect square.
We will call a right-angled triangle perfect if:
- it is a primitive right-angled triangle
- its hypotenuse is a perfect square
We will call a right-angled triangle super-perfect if:
- it is a perfect right-angled triangle
- its area is a multiple of the perfect numbers 6 and 28.
How many perfect right-angled triangles with $c ≤ {10}^{16}$ exist that are not super-perfect?