线性筛

https://www.luogu.org/problemnew/show/P1403

#include<bits/stdc++.h>
#define fi first
#define se second
#define INF 0x3f3f3f3f
#define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0)
#define pqueue priority_queue
#define NEW(a,b) memset(a,b,sizeof(a))
#define lowbit(x) ((x)&(-x))
const double pi=4.0*atan(1.0);
const int maxn=1e6+8;
typedef long long LL;
typedef unsigned long long ULL;
const LL mod=1e9+7;
const ULL base=1e7+7;
const double e=exp(1);
using namespace std;
int prime[maxn];
bool isnotprime[maxn]={1,1};
int d[maxn];
int f[maxn];
int tot=0;
void get_prime(int n){
    for(int i=2;i<=n;i++){
        if(!isnotprime[i]){
            prime[tot++]=i;
            d[i]=i;
        }
        for(int j=0;j<tot;j++){
            if(i*prime[j]>n) break;
            isnotprime[i*prime[j]]=1;
            d[i*prime[j]]=d[i];
            if(i%prime[j]==0) break;
        }
    }
}
int main(){
    fio;
    int n;
    cin>>n;
    f[1]=1;
    LL sum=1;
    get_prime(n);
    for(int i=2;i<=n;i++){
        int t=2;
        int j=i/d[i];
        int now=d[i];
        while(j%d[i]==0){
            j/=d[i];
            now*=d[i];
            t++;
        }
        //cout<<i<<' '<<now<<endl;
        if(now!=i)
        d[i]=now;
        else{
            d[i]=0;
            f[i]=t;
        }
    }
    for(int i=2;i<=n;i++){
        if(!isnotprime[i]){
            f[i]=2;
        }
        else if(d[i]){
            f[i]=f[d[i]]*f[i/d[i]];
        }
        sum+=f[i];
        //cout<<i<<' '<<f[i]<<' '<<d[i]<<endl;

    }
    cout<<sum<<endl;
}