Problem 70
Totient permutation

Euler's Totient function, φ(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, φ(9)=6.
The number 1 is considered to be relatively prime to every positive number, so φ(1)=1.

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

Find the value of n, 1 <n < 107, for which φ(n) is a permutation of n and the ratio n/φ(n) produces a minimum.

These problems are part of Project Euler and are licensed under CC BY-NC-SA 2.0 UK