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 and
-its area is a multiple of the perfect numbers $6$ and $28$.

How many perfect right-angled triangles with $c\le {10}^{16}$ exist that are not super-perfect?

ProjectEuler+ Problem Statement

The Project Euler problem is equivalent to the ProjectEuler+ challenge with $q=1$ and $n={10}^{16}$.