[题解]（gcd/欧拉函数）luogu_P2568_GCD

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
const int maxn=10000009;
int n;
int ck[maxn],prime[maxn],phi[maxn],tot;
long long sum[maxn];
void eular(int n){
    phi[1]=1;
    for(int i=2;i<=n;i++){
        if(!ck[i]){
            ck[i]=i,prime[++tot]=i;
            phi[i]=i-1;
        }
        for(int j=1;j<=tot;j++){
            if(prime[j]>ck[i] || i*prime[j]>n)break;
            ck[prime[j]*i]=prime[j];
            phi[i*prime[j]]=phi[i]*(i%prime[j]?prime[j]-1:prime[j]);
        }
    }
}
int main(){
    scanf("%d",&n);
    eular(n);
    for(int i=1;i<=n;i++)sum[i]=sum[i-1]+phi[i];
    long long ans=0;
    for(int i=1;i<=tot;i++){
        ans+=2*sum[n/prime[i]]-1;
    }
    printf("%lld\n",ans);
}