P1390 公约数的和

Posted 2022-08-12 war1111

 

#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;