# Commutativity between Base and Exponent

Let all the ordered pairs of distinct positive integer solutions of $$(a,b)$$ satisfying $$a^b = b^a$$ be $$(a_1, b_1), (a_2, b_2) ,\ldots , (a_n , b_n)$$.

Find $$\displaystyle \sum_{i=1}^n (a_i + b_i)$$.

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