Problem 53109. Easy Sequences 52: Non-squarable Rectangles
Any integer-sided rectangle can be cut into unit rectangles () and rearranged into sets of smaller rectangles. For example the rectangle can be broken as follows:
We call an integer rectangle as "squarable" if it can be can be broken (i.e. cut into unit rectangles and rearranged) into any number of non-unit squares of equal sizes. For example the rectangle can be broken into six squares. Therefore, the rectangle is squarable.
Integer rectangles that are not squarable are called "non-squarable". The rectangle, shown in the first example above, is a non-squarable rectangle. The complete set of non-squarable rectangles with area square units are as follows:
Create a program that calculates the total area of all non-squarable integer rectangles whose areas are less than or equal to a given area limit A.
For , the program should output:
NOTE: Reflections and rotations are not significant and should be counted only once.
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