【题解】51Nod 1594 莫比乌斯反演

 1 //
 2 //  main.cpp
 3 //  51nod
 4 //
 5 //  Created by gengyf on 2019/8/8.
 6 //  Copyright © 2019 yifan Geng. All rights reserved.
 7 //
 8 
 9 #include <iostream>
10 using namespace std;
11 namespace gengyf{
12 #define maxn 2000010
13 #define ll long long
14     inline int read(){
15         int f=1,x=0;char s=getchar();
16         while(s<‘0‘||s>‘9‘){if(s==‘-‘)f=-1;s=getchar();}
17         while(s>=‘0‘&&s<=‘9‘){x=x*10+s-‘0‘;s=getchar();}
18         return f*x;
19     }
20     ll w[maxn>>2],miu[maxn],phi[maxn],c[maxn],vis[maxn];
21     int n,T,t;ll ans;
22     void init(){
23         phi[1]=miu[1]=1;
24         for(int i=2;i<=maxn;i++){
25             if(!vis[i]){//如果是质数
26                 miu[++w[++t]=i]=-1;
27                 phi[i]=i-1;
28             }
29             for(int j=1,k;(k=i*w[j])<=maxn;j++){
30                 vis[k]=1;
31                 if(i%w[j]==0){
32                     phi[k]=phi[i]*w[j];
33                     miu[k]=0;break;
34                 }
35                 phi[k]=phi[i]*(w[j]-1);miu[k]=-miu[i];
36             }
37         }
38     }
39     ll F(int x){return c[x]*c[x];}
40     ll calc(int n){
41         memset(c,0,sizeof(c));
42         ans=0;
43         for(int i=1;i<=n;i++){
44             ++c[phi[i]];
45         }
46         for(int i=1;i<=n;i++)
47             for(int j=i+i;j<=n;j+=i){
48                 c[i]+=c[j];
49             }
50         for(int i=1;i<=n;i++){
51             if(miu[i])
52                 for(int j=1;i*j<=n;j++){
53                     ans+=F(i*j)*miu[i]*phi[j];
54                 }
55         }
56         return ans;
57     }
58     int main(){
59         init();
60         T=read();
61         while(T--){
62             n=read();
63             printf("%lld\n",calc(n));
64         }
65         return 0;
66     }
67 }
68 int main(){
69     gengyf::main();
70     return 0;
71 }