Find the number of positive integers n less than 1000 for which there exists a positive real number x such that n=x\lfloor x\rfloor.

Note: \lfloor x\rfloor is the greatest integer less than or equal to x.

Find the number of positive integers n less than 1000 for which there exists a positive real number x such that n=x\lfloor x\rfloor.

Note: \lfloor x\rfloor is the greatest integer less than or equal to x.