# Sreejato's ordered pairs

For positive integers $$x$$, let $$f(x)$$ be the number of ordered pairs of positive integers $$(a, b)$$ such that $\frac{1}{a} + \frac{1}{b} = \frac{1}{x}.$

Find the smallest possible value of $$N$$ such that $$N$$ is a prime power and $$f(N)= 13$$.

This problem is posed by Sreejato B.

Details and assumptions

A prime power is of the form $$p^n$$, where $$p$$ is a prime number and $$n$$ is a positive integer.

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