【模板】杜教筛

#include <cstdio>
#include <cstdlib>
#include <map>
#define ll long long
using namespace std;
const int N=6e6,M=6e6+10;
ll phi[M];
int prime[M],tot,vis[M],T,n,u[M];
map <ll,ll> wp;
map <int,int> wu;
inline char get()
{
    static char buf[1024];
    static int pos=0,size=0;
    if(pos==size)
    {
        size=fread(buf,1,1024,stdin);
        pos=0;
        if(!size) return EOF;
        else return buf[pos++];
    }
    else return buf[pos++];     
}
int read()
{
    int sum=0,fh=1;
    char ch=get();
    while(!(ch>=‘0‘ && ch<=‘9‘))
    {
        if(ch==‘-‘) fh=-1;
        ch=get();
    }
    while(ch>=‘0‘ && ch<=‘9‘ && ch!=EOF) sum=sum*10+ch-48,ch=get();
    return sum*fh;
}
void init()
{
    phi[1]=u[1]=1;
    for(int i=2;i<=N;i++)
    {
        if(!vis[i]) phi[i]=i-1,prime[++tot]=i,u[i]=-1;
        for(int j=1;j<=tot && prime[j]<=N/i;j++)
        {
            int x=prime[j]*i;
            vis[x]=1;
            if(i%prime[j]==0)
            {
                phi[x]=phi[i]*prime[j];
                break;
            }
            else u[x]=-u[i],phi[x]=phi[i]*(prime[j]-1);
        }
        u[i]+=u[i-1],phi[i]+=phi[i-1];
    }
}
int getu(int x)
{
    if(x<=N) return u[x];
    if(wu[x]) return wu[x];
    int ans=1;
    for(int l=2,r;l<=x;l=r+1)
    {
        r=x/(x/l);
        ans-=(r-l+1)*getu(x/l);
    }
    return wu[x]=ans;
}
ll getphi(ll x)
{
    if(x<=N) return phi[x];
    if(wp[x]) return wp[x];
    ll ans=x*(x+1)/2;
    for(ll l=2,r;l<=x;l=r+1)
    {
        r=x/(x/l);
        ans-=(r-l+1)*getphi(x/l);
    }
    return wp[x]=ans;
}
int main()
{
    init();
    T=read();
    while(T--)
    {
        n=read();
        printf("%lld %d\n",getphi(n),getu(n));
    }
    return 0;
}