A Rectangle which cannot be built up of Squares all of different sizes is called an imperfect rectangle. A Rectangle which can be built up of Squares all of different sizes is called perfect. The number of perfect rectangles of orders 8, 9, 10, ... are 0, 2, 6, 22, 67, 213, 744, 2609, ... (Sloane's A002839) and the corresponding numbers of imperfect rectangles are 0, 1, 0, 0, 9, 34, 103, 283, ... (Sloane's A002882).

**References**

Sloane, N. J. A. Sequences A002839/M1658 and A002882/M4614 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html.

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1999-05-26