/*

Counting Fractions

Consider the fraction, n/d, where n and d are positive integers. If n<d and HCF(n,d)=1, it is called a reduced proper fraction.

If we list the set of reduced proper fractions for d ≤ 8 in ascending order of size, we get:

1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8

It can be seen that there are 21 elements in this set.

How many elements would be contained in the set of reduced proper fractions for d ≤ 1,000,000?

*/

#include <bits/stdc++.h>

using namespace std;

const int MAX = 1000000;

int main(){

    cout << "Hello this is Patrick" << endl;
    auto start = chrono::high_resolution_clock::now();

    vector<int> phi(MAX + 1);
    for(int i = 2; i <= MAX; ++i){
        phi[i] = i;
    }

    long long sum = 0;

    for(int i = 2; i <= MAX; ++i){
        if(phi[i] == i){
            for(int j = i; j <= MAX; j += i){
                phi[j] = phi[j] / i * (i - 1);
            }
        }
        sum += phi[i];
    }

    cout << sum << endl;

    auto duration = chrono::duration_cast<chrono::milliseconds>(chrono::high_resolution_clock::now() - start);
    cout << (float)duration.count()/1000 << endl;
    return 0;
}