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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