线性欧拉筛

Posted 2021-12-01 adventurer-h

//欧拉函数 小于等于 n 且与n互质的正整数个数 
#include <bits/stdc++.h>

using namespace std;

const int N = 100001;

int n,p;
int prime[N],phi[N],mark[N];

int main(){
    cin >> n;
    phi[1] = 1;
    for(int i = 2; i <= n; ++i){
        if(!mark[i]){ 
            prime[++p] = i;
            phi[i] = i - 1;
        } 
        for(int j = 1; j <= p; ++j){
            if(i * prime[j] > n) break;
            mark[i * prime[j]] = 1;
            if(i % prime[j] == 0){
                phi[i * prime[j]] = prime[j] * phi[i];      //欧拉积性 if(a|b) phi(ab) = a * phi(b); 
                break;
            }
            else phi[i * prime[j]] = phi[i] * phi[prime[j]];//欧拉积性 if(a互质b) phi(ab) = phi(a) * phi(b); 
        }
    }
    for(int i = 1; i <= p; ++i) cout << prime[i] << " ";
    cout << endl;
    for(int i = 1; i <= n; ++i) cout << phi[i] << " ";    
    return 0;
}