Let's call this as the Mohanty's Triangle!

Logic Level 4

A triangle like the one shown above is constructed with the numbers from 1 to 2015 in the first row. Each number in the triangle, except those in the first row, is the sum of the two numbers above it. Let \(N\) be the number that occupies the lowest vertex of the triangle.

If the prime factorization of \(N\) is \(p_1^{k_1} \cdot p_2^{k_2} \cdot p_3^{k_3},\) find the value of \(p_1 + p_2 + p_3 + k_1 + k_2 + k_3\).

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