# 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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