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Problem #364

Egyptian equation II
 Public ★(x15) 09/23/16 by Philippe_57721 7xp Programming 71.4%

Let the diophantine equation $\frac{1}{x} + \frac{1}{y} = \frac{1}{n}$ with $x \le y$

How many solutions are there for $n=1000000!$ ?

As the answer is a BIG number, use the following condensed representation:
(First 10 digits)[(number of remaining digits](Last 10 digits]

For instance, for 2^127, the representation is: 1701411834[19]5884105728

Example: $8583170787[2]5400804688 \textrm{ for } n = 100!$

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