--description--

In the following equation $x$, $y$, and $n$ are positive integers.

$$\frac{1}{x} + \frac{1}{y} = \frac{1}{n}$$

For a limit $L$ we define $F(L)$ as the number of solutions which satisfy $x < y ≤ L$.

We can verify that $F(15) = 4$ and $F(1000) = 1069$.

Find $F({10}^{12})$.

--hints--

diophantineReciprocalsThree() should return 5435004633092.

assert.strictEqual(diophantineReciprocalsThree(), 5435004633092);

--seed--

--seed-contents--

function diophantineReciprocalsThree() {

  return true;
}

diophantineReciprocalsThree();

--solutions--

// solution required