Jigsaw Numbers

Jigsaw puzzles come in very different shapes and sizes, but there are some constraints.

We will call a number \(N\) a jigsaw number if it is the number of pieces of a jigsaw puzzle whose length is less than twice its width. For instance, 48 is a jigsaw number because \(48 = 8\times 6\) and \(8 < 2\cdot 6\); but 32 is not a jigsaw number because its decompositions \(32\times1\), \(16\times2\), or \(8\times4\) do not have a length less than twice its width.

How many jigsaw numbers \(N\) are there such that \(1000 < N < 10000\)?

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