In a certain problem, the complexity of my algorithm is O(n*sum_of_factors(n)), I want to get a simple bound for the complexity. Obviously one bound is O(n^3), since there can be n factors each with maximum value n, a better bound is O(n^2*sqrt(n)) since a number can have 2*sqrt(n) factors.

Please help me to give a better bound in terms of simpler functions of n, (simple is defined here as stuff you can find on a standard scientific calculator).