luoguP4213（杜教篩）

題目鏈接：https://www.luogu.org/problemnew/show/P4213

思路：杜教板子題，這題卡常了，如果有單純杜教篩用了兩次還跑的賊快的，希望告訴我一聲emmm

#include <cstdio>
#include <cstdlib>
#include <cassert>
#include <cstring>
#include <bitset>
#include <cmath>
#include <cctype>
#include <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <queue>
#include <map>
#include <set>
#include <sstream>
#include <iomanip>
#include <unordered_map>
using namespace std;
typedef long long ll;
typedef vector<long long> VI;
typedef unsigned long long ull;
const ll inff = 0x3f3f3f3f3f3f3f3f;
#define FOR(i,a,b) for(int i(a);i<=(b);++i)
#define FOL(i,a,b) for(int i(a);i>=(b);--i)
#define SZ(x) ((long long)(x).size())
#define REW(a,b) memset(a,b,sizeof(a))
#define inf int(0x3f3f3f3f)
#define si(a) scanf("%d",&a)
#define sl(a) scanf("%lld",&a)
#define sd(a) scanf("%lf",&a)
#define ss(a) scanf("%s",a)
#define mod ll(1e9+7)
#define pb push_back
#define eps 1e-10
#define lc d<<1
#define rc d<<1|1
#define Pll pair<ll,ll>
#define P pair<int,int>
#define pi acos(-1)
int tot,pr[1000008],mu[6000008];
ll phi[6000008],n;
bool p[6000008];
unordered_map<int,ll>w1;
unordered_map<int,int>w2;
void gphimu(int n)
{
    phi[1]=1,p[1]=1,mu[1]=1;
    FOR(i,2,n)
    {
        if(!p[i]) p[i]=1,pr[++tot]=i,phi[i]=i-1,mu[i]=-1;
        for(int j=1;j<=tot&&pr[j]*i<=n;j++)
        {
            p[i*pr[j]]=1;
            if(i%pr[j]==0) {phi[i*pr[j]]=phi[i]*pr[j];mu[i*pr[j]]=0;break;}
            phi[i*pr[j]]=phi[i]*(pr[j]-1),mu[i*pr[j]]=-mu[i];
        }
    }
    FOR(i,1,n) mu[i]+=mu[i-1],phi[i]+=phi[i-1];
}
ll djsphi(int x)
{
    if(x<=6000000) return phi[x];
    if(w1.count(x)) return w1[x];
    ll ans=1ll*x*(x+1)>>1ll;
    for(int l=2,r;l<=x;l=r+1)
    {
        r=min(x/(x/l),x);
        ans-=(r-l+1)*djsphi(x/l);
    }
    return w1[x]=ans;
}
int djsmu(int x)
{
    if(x<=6000000) return mu[x];
    if(w2.count(x)) return w2[x];
    int ans=1;
    for(int l=2,r;l<=x;l=r+1)
    {
        r=min(x/(x/l),x);
        ans-=(r-l+1)*djsmu(x/l);
    }
    return w2[x]=ans;
}
int main()
{
    cin.tie(0);
    cout.tie(0);
    gphimu(6000000);
    int t;
    cin>>t;
    while(t--)
    {
        si(n);
        printf("%lld %d\n",djsphi(n),djsmu(n));
    }
    return 0;
}