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Diophantine reciprocals III

Problem 454

Published on Saturday, 11th January 2014, 07:00 pm; Solved by 208

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

1

x
+
1

y
=
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(1012).