Let Unparsed notation: f_\max(n) be the largest $m$ such that $\phi(m) = n$, and Unparsed notation: f_\min(n) be the smallest such $m$, where $\phi$ is Euler's totient function. Investigate Unparsed notation: \max_{n\leq x}\frac{f_\max(n)}{f_\min(n)}.