Magical function

Magical function

I did not understand why Euler function, first Tuen

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll maxn=4e6+5;
const ll MAX=1e9;
ll P[maxn];
ll phi[maxn];
ll A[maxn];
bool f[maxn];
ll K=0;
void init()
{
    phi[1]=1;
    for(int i=2; i<maxn; i++)
    {
        if(!f[i])
        {
            P[K++]=i;
            phi[i]=i-1;
        }
        for(int j=0; j<K&&i*P[j]<maxn; j++)

        {
             phi[i*P[j]]=phi[i]*(i%P[j]?P[j]-1:P[j]);
            f[i*P[j]]=1;
            if(i%P[j]==0)
            {
                break;
            }
        }
    }
    
}

int main()
{
    int T;
    init();
    scanf("%d",&T);
    ll x;
    ll ans;
    while(T--)
    {
        scanf("%lld",&x);
        ans=0;
        ll t=sqrt(x)+1,d;
        while(t)
        {

            ans+=x/(t*t)*phi[t];
            t--;
        }
        cout<<ans<<'\n';

    }
}