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If you do the factorization properly it will not TL.
So first find all primes in the range [2, sqrt(n) ] using
http://en.wikipedia.org/wiki/Sieve_of_Eratosthene.
Now you have to find the number of the divisors of n, then count the divisors of the form x^2, x^3,..., x^k(where x divides n), and add ...