Totient maximum

Euler's Totient function, \( \phi(n) \) [sometimes called the phi function], is defined as the number of positive integers not exceeding n which are relatively prime to n. For example, as \( 1 \), \( 2 \), \( 4 \), \( 5 \), \( 7 \), and \( 8 \), are all less than or equal to nine and relatively prime to nine, \( \phi(9)=6 \).

$n$	Relatively Prime	$\phi(n)$	$n/\phi(n)$
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 \( \frac{n}{\phi(n)} \) for \( n\leq 10 \).

Find the value of \( n\leq 1,000,000 \) for which \( \frac{n}{\phi(n)} \) is a maximum.