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Suppose S is a set of positive integers, none of which has a prime factor greater than 20. The greatest common factor of any two

Suppose S is a set of positive integers, none of which has a prime factor greater than 20. The greatest common factor of any two distinct elements of S is an integer greater than 1 and is not divisible by the square of any prime number.

What is the greatest possible number of elements in S?

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