SPOJ—VLATTICE Visible Lattice Points（莫比乌斯反演）

 1 #include<iostream>
 2 #include<algorithm>
 3 #include<cstring>
 4 #include<cstdio>
 5 #include<sstream>
 6 #include<vector>
 7 #include<stack>
 8 #include<queue>
 9 #include<cmath>
10 #include<map>
11 #include<set>
12 using namespace std;
13 typedef long long ll;
14 typedef pair<int,int> pll;
15 const int INF = 0x3f3f3f3f;
16 const int maxn = 1000000 + 5;
17 
18 bool check[maxn];
19 int prime[maxn];
20 int mu[maxn];
21 ll sum[maxn];
22 
23 void Mobius()
24 {
25     memset(check, false, sizeof(check));
26     mu[1] = 1;
27     int tot = 0;
28     for (int i = 2; i <= maxn; i++)
29     {
30         if (!check[i])
31         {
32             prime[tot++] = i;
33             mu[i] = -1;
34         }
35         for (int j = 0; j < tot; j++)
36         {
37             if (i * prime[j] > maxn)
38             {
39                 break;
40             }
41             check[i * prime[j]] = true;
42             if (i % prime[j] == 0)
43             {
44                 mu[i * prime[j]] = 0;
45                 break;
46             }
47             else
48             {
49                 mu[i * prime[j]] = -mu[i];
50             }
51         }
52     }
53     sum[0]=0;
54     for(int i=1;i<maxn;i++)
55         sum[i]=sum[i-1]+mu[i];
56     return ;
57 }
58 
59 ll compute1(int n)
60 {
61     ll tmp=0;
62     for(int i=1,last=0;i<=n;i=last+1)
63     {
64         last=n/(n/i);
65         tmp+=(sum[last]-sum[i-1])*(n/i)*(n/i)*(n/i);
66     }
67     return tmp;
68 }
69 
70 ll compute2(int n)
71 {
72     ll tmp=0;
73     for(int i=1,last=0;i<=n;i=last+1)
74     {
75         last=n/(n/i);
76         tmp+=(sum[last]-sum[i-1])*(n/i)*(n/i);
77     }
78     return tmp;
79 }
80 
81 int n, m;
82 
83 int main()
84 {
85     //freopen("in.txt","r",stdin);
86     Mobius();
87     int T;
88     scanf("%d",&T);
89     while(T--)
90     {
91         scanf("%d",&n);
92         printf("%lld\n",compute1(n)+compute2(n)*3+3);
93     }
94     return 0;
95 }