C-Plus-Plus/math/eulers_totient_function.cpp

#include<bits/stdc++.h>

using namespace std;
typedef long long int ll;

/**

Euler Totient Function also know as phi function.

phi(n) = phi(p1^a1).phi(p2^a2)...
where p1, p2,... are prime factor of n.

3 Euler's Property:
1. phi(prime_no) = prime_no-1
2. phi(prime_no^k) = (prime_no^k - prime_no^(k-1))
3. phi(a,b) = phi(a). phi(b) where a and b are relative primes.

Applying this 3 property on the first equation.
phi(n) = n. (1-1/p1). (1-1/p2). ...
where p1,p2... are prime factors.

Hence Implementation in O(sqrt(n)).

*/

ll phiFunction(ll n){
    ll res = n;
    for(ll i=2;i*i<=n;i++){
        if(n%i==0){
            while(n%i==0){
                n/=i;
            }
            res-=res/i;
        }
    }
    if(n>1)res-=res/n;
    return res;
}

int main(){
    ll t;
    cin>>t;
    while(t--){
        ll n;
        cin>>n;
        cout<<phiFunction(n)<<endl;
    }
}