Euler's totient function, $\varphi (n)$ [sometimes called the phi function], is used to determine the number of positive numbers less than or equal to $n$ which are relatively prime to $n$. For example, as $1,2,4,5,7$, and $8$, are all less than nine and relatively prime to nine, $\varphi (9)=6$.
The number $1$ is considered to be relatively prime to every positive number, so $\varphi (1)=1$.

Interestingly, $\varphi (87109)=79180$, and it can be seen that $87109$ is a permutation of $79180$.

Find the value of $n$, $1<n<{10}^7$, for which $\varphi (n)$ is a permutation of $n$ and the ratio $n/\varphi (n)$ produces a minimum.