Product-perfect Numbers

A number, greater than or equal to 2, is called product-perfect if it is equal to the product of all of its proper divisors. For example, \( 6 = 1 \times 2 \times 3 \), hence \(6\) is product perfect. How many product-perfect numbers are there below \(50\)?

Details and assumptions

A proper divisor of a number \(N\) is a positive integer less than \( N \) that divides \(N\).

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