# Mathematics Q 2

Let $$1,a_1,a_2, \ldots , a_k$$ be all the positive divisors of $$N = { 2 }^{ 74207280 }( { 2 }^{ 74207281 }-1 )$$ arranged in ascending order. And let $$T$$ denote the number of ways to express $$N$$ as the product of two coprime factors.

Compute $$\displaystyle K + \left(\sum_{i=1}^K \dfrac1{a_i} \right) + T$$.

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