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=1×2×3 6 = 1 \times 2 \times 3 , hence 66 is product perfect. How many product-perfect numbers are there below 5050?

Details and assumptions

A proper divisor of a number NN is a positive integer less than N N that divides NN.

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