P1390 公约数的和

 

#include <iostream>
#include <cstdio>
#include <queue>
#include <algorithm>
#include <cmath>
#include <cstring>
#define inf 2147483647
#define N 2000010
#define mod 1000000007
#define p(a) putchar(a)
#define For(i,a,b) for(long long i=a;i<=b;++i)
//by war
//2019.8.21
using namespace std;
long long n,tot[N],num,cnt,ans,temp;
long long prime[N],mu[N];
bool vis[N];
void in(long long &x){
    long long y=1;char c=getchar();x=0;
    while(c<'0'||c>'9'){if(c=='-')y=-1;c=getchar();}
    while(c<='9'&&c>='0'){ x=(x<<1)+(x<<3)+c-'0';c=getchar();}
    x*=y;
}
void o(long long x){
    if(x<0){p('-');x=-x;}
    if(x>9)o(x/10);
    p(x%10+'0');
}

void Euler(){
    mu[1]=1;
    For(i,2,2e6){
        if(!vis[i]) prime[++cnt]=i,mu[i]=-1;
        for(long long j=1;j<=cnt&&i*prime[j]<=2e6;j++){
            vis[i*prime[j]]=1;
            if(i%prime[j]==0){
                mu[i*prime[j]]=0;
                break;
            }
            mu[i*prime[j]]=-mu[i];
        }
    }
}

signed main(){
    in(n);
    Euler();
    For(i,1,n){
        temp=0;
        for(long long d=i;d<=n;d+=i){
            num=n/d;
            temp+=mu[d/i]*num*(num-1)/2;
        }
        ans+=temp*i;
    }
    o(ans);
    return 0;
}