Problem 55345. Easy Sequences 68: Factorial Rectangles
I'll celebrate my comeback to Cody with this one easy problem...
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The rectangle below is special:
Its area is
which equal to
. We call such rectangle a factorial rectangle, which is an integer-sided rectangle with an area equal to a factorial number.
In this problem, we want to know how many are these factorial rectangles.
For a given integer n, we define the function
as the number of factorial rectangles with area
The factorial rectangles with area
are as follows:
, with rotations not allowed. Hence, 
Write a function that will calculate
, defined as follows:
For
, we are given:
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