Question 914653: A proper divisor of a positive integer is a positive integral divisor other than 1 and itself. A positive integer greater than 1 is a sweet # if the product of its distinct proper divisors is equal to the # itself. List the 10 smallest sweet numbers.
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Suppose the proper divisors of n are  where  . Then we have  ,  , and so on. We want the product of the d_i's to equal n, and this occurs if and only if n has two proper divisors (excluding 1), or when n has exactly four divisors. This occurs if and only if n is a product of two different primes, or n is the cube of a prime.
First 10 sweet numbers: 6, 8, 10, 14, 15, 21, 22, 26, 27, 33
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