Diophantine reciprocals III

Published on Saturday, 11th January 2014, 07:00 pm; Solved by 359;
Difficulty rating: 50%

Problem 454

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

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

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

We can verify that F(15) = 4 and F(1000) = 1069.
Find F(1012).