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.
by
Calvin Lin
