/* 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.

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.

*/

#include <bits/stdc++.h>

using namespace std;

const int MAX = 1000000;

vector<int> sieve(int n){
    vector<bool> numbers(n+1, true);
    vector<int> result;

    int i = 2;
    while(i <= n){
        if(numbers[i]){
            result.push_back(i);

            int j = 2 * i;
            while(j <= n){
                numbers[j] = false;
                j += i;
            }
        }
        ++i;
    }

    return result;
}

vector<int> prime_terms(int n){
    vector<int> result;

    if(n % 2 == 0){
        result.push_back(2);

        while(n % 2 == 0){
            n /= 2;
        }
    }

    for(int i = 3; i <= sqrt(n); i += 2){
        if(n % i == 0){
            result.push_back(i);

            while(n % i == 0){
                n /= i;
            }
        }
    }

    if(n > 2){
        result.push_back(n);
    }

    return result;
}

int main(){

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

    vector<float> n_phi(MAX + 1, 0);
    auto primes = sieve(MAX);

    for(auto p : primes){
        n_phi[p] = 1 + 1 / ((float)p - 1);
    }

    int n_max = 0;
    float n_phi_max = 0;

    for(size_t i = 2; i < n_phi.size(); ++i){
        if(n_phi[i] == 0){
            auto terms = prime_terms(i);
            float acc = 1;

            for(int t : terms){
                acc *= n_phi[t];
            }
            n_phi[i] = acc;

            if(n_phi_max < acc){
                n_max = i;
                n_phi_max = acc;
            }
        }

        // cout << i << " " << n_phi[i] << endl;
    }

    cout << n_max << endl;

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