id	title	challengeType	forumTopicId	dashedName
5900f5331000cf542c510045	Problem 454: Diophantine reciprocals III	5	302127	problem-454-diophantine-reciprocals-iii

--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);

function diophantineReciprocalsThree() {

  return true;
}

diophantineReciprocalsThree();

// solution required