Totient permutation

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 \( \frac{n}{\varphi(n)} \) produces a minimum.