# Must Have A Lot Of Factors

Define a cool number as a positive integer $$n \geq 2$$ that satisfies the following:

For all pairs of factors $$a, b$$ of $$n$$ satisfying $$\gcd (a,b)=1$$, then $$a+b-1$$ is also a factor of $$n$$.

Find the number of cool numbers under 1000.

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