p4213 【模板】杜教筛(Sum)

传送门

分析

我们知道

$\varphi * 1 = id$

$\mu * 1 = e$

杜教筛即可

代码

#include<iostream>
#include<cstdio>
#include<cstring>
#include<string>
#include<algorithm>
#include<cctype>
#include<cmath>
#include<cstdlib>
#include<queue>
#include<ctime>
#include<vector>
#include<set>
#include<map>
#include<stack>
#include<unordered_map>
using namespace std;
const int N = 5e6;
unordered_map<int,long long>phi;
unordered_map<int,int>mu;
unordered_map<int,bool>visp,vism;
long long _p[N+];
int _m[N+];
int cnt,p[N];
bool is[N+];
inline long long get_phi(int x){
    if(x<=N)return _p[x];
    if(visp[x])return phi[x];
    long long res=(long long)x*(x+)/;
    int le=,ri;
    for(;le<=x;le=ri+){
      ri=x/(x/le);
      res-=(ri-le+)*get_phi(x/le);
    }
    visp[x]=;return phi[x]=res;
}
inline int get_mu(int x){
    if(x<=N)return _m[x];
    if(vism[x])return mu[x];
    int res=,le=,ri;
    for(;le<=x;le=ri+){
      ri=x/(x/le);
      res-=(ri-le+)*get_mu(x/le);
    }
    vism[x]=;return mu[x]=res;
}
inline void go(){
    register int i,j,k;
    _p[]=_m[]=;
    for(i=;i<=N;++i){
      if(!is[i])p[++cnt]=i,_m[i]=-,_p[i]=i-;
      for(j=;j<=cnt,i*p[j]<=N;++j){
          is[p[j]*i]=;
          if(i%p[j]==){
            _m[i*p[j]]=;
            _p[i*p[j]]=_p[i]*p[j];
            break;
          }
          _m[i*p[j]]=-_m[i];
          _p[i*p[j]]=_p[i]*(p[j]-);
      }
    }
    for(i=;i<=N;++i)_p[i]+=_p[i-],_m[i]+=_m[i-];
}
int main(){
    int n,t;
    scanf("%d",&t);
    go();
    while(t--){
      scanf("%d",&n);
      printf("%lld %d\n",get_phi(n),get_mu(n));
    }
    return ;
}