Problem 69: Totient maximum
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.
Test
{{test}}Console output