Problem 231: The prime factorisation of binomial coefficients

The binomial coefficient 10C3 = 120.

120 = 23 × 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 10C3 is 14.

Find the sum of the terms in the prime factorisation of 20000000C15000000.

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