831 B
831 B
Euler's Totient function, phi(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, 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 n/phi(n)
for n <= 10
.
Find the value of n <= 1,000,000
for which n/phi(n)
is a maximum.