[luogu1390]公约数的和

 1 #include<bits/stdc++.h>
 2 using namespace std;
 3 #define N 2000005
 4 long long n,ans,f[N],vis[N],p[N];
 5 void mobies(int n){
 6     f[1]=1;
 7     for(int i=2;i<=n;i++){
 8         if (!vis[i])f[p[++p[0]]=i]=i-1;
 9         for(int j=1;j<=p[0];j++){
10             if (p[j]*i>n)break;
11             vis[i*p[j]]=1;
12             if (i%p[j]==0)f[i*p[j]]=f[i]*p[j];
13             else f[i*p[j]]=f[i]*(p[j]-1);
14         }
15     }
16     for(int i=2;i<=n;i++)f[i]+=f[i-1];
17 }
18 int main(){
19     mobies(N-5);
20     scanf("%lld",&n);
21     for(int i=1,j;i<=n;i=j+1){
22         j=n/(n/i);
23         ans+=(f[j]-f[i-1])*(n/i)*(n/i);
24     }
25     printf("%lld",(ans-n*(n+1)/2)/2);
26 }

 

来源：https://www.cnblogs.com/PYWBKTDA/p/11272034.html