3944: Sum（杜教筛）

/*
    就相当于111112222222333333333每个数都有相同的一坨，然后只算出一坨的第一个数，乘个他的次数，直接跳到下一坨
*/ 
#include<iostream>
#include<cstdio>
#include<cstring>
#include<map>
#define maxn 5000005
#define N 5000000
using namespace std;
int p[maxn],mu[maxn],cnt;
long long phi[maxn];
bool vis[maxn];
void prepare(){
    memset(vis,0,sizeof(vis));
    phi[1]=1;mu[1]=1;
    for(int i=2;i<=N;i++){
        if(!vis[i])p[++cnt]=i,phi[i]=i-1,mu[i]=-1;
        for(int j=1;j<=cnt&&i*p[j]<=N;j++){
            vis[i*p[j]]=1;
            if(i%p[j]==0){
                phi[i*p[j]]=phi[i]*p[j];
                mu[p[j]*i]=0;break;
            }
            phi[i*p[j]]=phi[i]*phi[p[j]];
            mu[i*p[j]]=-mu[i];
        }
    }
    for(int i=1;i<=N;i++)phi[i]+=phi[i-1],mu[i]+=mu[i-1];
}
map<long long,long long>lst_phi;
map<long long,int>lst_mu;
long long sum_phi(long long n){
    if(n<=N)return phi[n];
    if(lst_phi[n]!=0)return lst_phi[n];
    long long res=n*(n+1)/2;
    for(long long i=2,nxt;i<=n;i=nxt+1){
        nxt=n/(n/i);
        res-=sum_phi(n/i)*(nxt-i+1);
    }
    return lst_phi[n]=res;
}
int sum_mu(long long n){
    if(n<=N)return mu[n];
    if(lst_mu[n]!=0)return lst_mu[n];
    int res=1;
    for(long long i=2,nxt;i<=n;i=nxt+1){
        nxt=n/(n/i);
        res-=sum_mu(n/i)*(nxt-i+1);
    }
    return lst_mu[n]=res;
}
int main(){
    freopen("Cola.txt","r",stdin);
    prepare();
    int Q;scanf("%d",&Q);
    while(Q--){
        int n;scanf("%d",&n);
        cout<<sum_phi(n)<<‘ ‘<<sum_mu(n)<<endl;
    }
}