Affixing squares

Starting with a square of the size \(1 \times 1\), you may do the following operation any number of times (including none at all): choose one side of the rectangle you have and affix a square to that side, with length equal to that side. The image above shows one possibility.

Determine the number of ordered pairs of integers \((l,w)\), with \(1 \le l,w \le 100\), such that you can obtain a rectangle of size \(l \times w\).

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