Find the number of integers less than or equal to that are equal to for some choice of distinct positive integers and .
We notice that .
Therefore a number can be expressed in the given form if and only if can be expressed as the product of two distinct positive integers which are greater than . However, these are simply composite numbers between and inclusive who are not equal to the square of a prime number. There are primes between and inclusive. We must also exclude , , , and .
Thus, the answer is
The problems on this page are the property of the MAA's American Mathematics Competitions