A positive integer n is called a regular number, if and only if there exist a non-negative integer k, such that . For some reason, such a number is also refered to as an ugly number. Below are the first few regular numbers:
We say that an integer-sided rectangle is a "regular" rectangle if its area is a regular number. In the figure below, the red-colored rectanges are regular, while the blue ones are not.
All regular rectangles whose areas are less than equal to are listed below:
And their total area is:
For a given area limit a, find the total area of all regular rectangles with areas less than equal a.
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