Inspired by Satyajit Mohanty

\[\large{a^{a^{5}}=b^{b}}\]

There exist \(n \geq 1\) pair(s) of positive integers \((a_{i},b_{i})\) with \(a_{i},b_{i} > 1\) such that the above equation is satisfied.

Find \(\displaystyle \sum_{i=1}^{n} (a_{i}+b_{i})\).


Inspiration.

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