The only composite numbers between 16 and 20 are 18 and 20. Since you mentioned that you are greater than 16 but less than 20, the only candidate is 18.
The factors of 18 are 1, 2, 3, 6, 9, and 18. Among these, 2 and 4 (which is double 2) fit the clue you provided, where one of the factors is a number and the other is that number doubled.
Therefore, the composite number you are thinking of is 18.
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