## Totient maximum

### Problem 69

Published on Friday, 7th May 2004, 06:00 pm; Solved by 16210

Euler's Totient function, φ(n) [sometimes called the phi function], is used to determine the number of numbers less than 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.

n | Relatively Prime | φ(n) | n/φ(n)
2 | 1 | 1 | 2
3 | 1,2 | 2 | 1.5
4 | 1,3 | 2 | 2
5 | 1,2,3,4 | 4 | 1.25
6 | 1,5 | 2 | 3
7 | 1,2,3,4,5,6 | 6 | 1.1666...
8 | 1,3,5,7 | 4 | 2
9 | 1,2,4,5,7,8 | 6 | 1.5
10 | 1,3,7,9 | 4 | 2.5

It can be seen that n=6 produces a maximum n/φ(n) for n 10.

Find the value of n 1,000,000 for which n/φ(n) is a maximum.