Project Euler Problem 69
First I brute forced to see if I noticed a pattern. Having noticed one, I implemented it as a solution and found it to
be the right answer.
Problem:
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.
1.8.11
