欧拉函数

1、分解质因数

/*
f(n) : 1 - n 中与n互质的个数(gcd(a, b) = 1)
n = p1^a1.p2^a2...pn^an
f(n) = n * (1 - 1/p1)(1 - 1/p2)...(1 - 1/pn)
*/
#include <bits/stdc++.h>
using namespace std;

int div_ola(int x){
    int res = x;
    for(int i = 2; i <= x / i; ++i){
        if(x % i == 0){
            res = res / i * (i - 1);
            while(x % i == 0) x /= i;
        }
    }
    if(x > 1) res = res / x * (x - 1);
    return res;
}

signed main(){
    int n;
    cin >> n;
    cout << div_ola(n);

    return 0;
}

2、筛法

#include <bits/stdc++.h>
using namespace std;

const int N = 1e5 + 10;
int cnt, p[N], st[N], e[N];

void div_ola(int n){
    e[1] = 1;
    for(int i = 2; i <= n; ++i){
        if(!st[i]){
            p[cnt++] = i;
            e[i] = i - 1;
        }
        for(int j = 0; p[j] <= n / i; ++j){
            int t = p[j] * i;
            st[t] = true;
            if(i % p[j] == 0){
                e[t] = e[i] * p[j];
                break;
            }
            e[t] = e[i] * (p[j] - 1);
        }
    }
}

signed main(){
    div_ola(100);
    for(int i = 1; i <= 100; ++i) cout << e[i] << " ";

    return 0;
}