--description--

There are several ways to write the number $\frac{1}{2}$ as a sum of inverse squares using distinct integers.

For instance, the numbers {2,3,4,5,7,12,15,20,28,35} can be used:

$$\frac{1}{2} = \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \frac{1}{5^2} + \frac{1}{7^2} + \frac{1}{{12}^2} + \frac{1}{{15}^2} + \frac{1}{{20}^2} + \frac{1}{{28}^2} + \frac{1}{{35}^2}$$

In fact, only using integers between 2 and 45 inclusive, there are exactly three ways to do it, the remaining two being: {2,3,4,6,7,9,10,20,28,35,36,45} and {2,3,4,6,7,9,12,15,28,30,35,36,45}.

How many ways are there to write the number $\frac{1}{2}$ as a sum of inverse squares using distinct integers between 2 and 80 inclusive?

--hints--

sumInverseSquares() should return 301.

assert.strictEqual(sumInverseSquares(), 301);

--seed--

--seed-contents--

function sumInverseSquares() {

  return true;
}

sumInverseSquares();

--solutions--

// solution required