Problem 231

The prime factorisation of binomial coefficients

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}.

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