Project Euler

Problem #231

The binomial coefficient ^(10)C_(3) = 120.
120 = 2^(3) × 3 × 5 = 2 × 2 × 2 × 3 × 5, and 2 + 2 + 2 + 3 + 5 = 14.
So the sum of the terms in the prime factorisation of ^(10)C_(3) is 14.

Find the sum of the terms in the prime factorisation of ^(20000000)C_(15000000).