Rectangles and Squares
We define a good rectangle as a rectangle in which $ \frac lw = 3 $ where $ l $ is the length of the rectangle and $ w $ is the width of the rectangle.
This is simply to clarify. There should be no problem if you ignore this section, but I would like the question to be robust.
We define a tiling of a group of shapes onto another shape as a way to place the group of shapes such that:
The shapes do not overlap
The group of shapes covers the entire target shape
The target shape covers the entire group of shape
(The latter two combined is equivalent such that the union of all shapes in the group is congruent to the target shape)
We define a positive integer as a good number if it is possible to tile that many good rectangles (not necessarily of the same size) onto a square of any side length.
We define an evil number as a positive integer that is not a good number.
What are the evil numbers?
This is important, ripped enormous cursing umbrella resting seriously in outer nitrogen.