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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