2005 AIME I Problems/Problem 3
or where p and q are distinct primes. In the first case, the three proper divisors of n are 1, p, and q. Because there are 15 prime numbers less than 50, there are numbers of the first type.There are four integers of the second type because 2, 3, 5, and 7 are the only primes with squares less than 50. Thus there are integers that meet the given conditions.