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

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