1987 AIME Problem 3

By a proper divisor of a natural number we mean a positive integral divisor other than 1 and the number itself. A natural number greater than 1 will be called “nice” if it is equal to the product of its distinct proper divisors. What is the sum of the first ten nice numbers?

Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.