There is some analysis of this problem in this page:

http://www.cis.udel.edu/~breech/contest/problems/thoughts - see "Problem 2"

The interesting part is: "You only need to go to sqrt(x). If you find a d such that x%d == 0, then you know that d and x/d are both divisors. You do have to make a quick check to make sure that d and x/d are not equal before summing both".