Sreejato's ordered pairs

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

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

This problem is posed by Sreejato B.

Details and assumptions

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

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