Problem 218: Perfect right-angled triangles

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≤1016 exist that are not super-perfect?

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