【欧拉函数】BZOJ2190-[SDOI2012]longge的数学问题

 1 #include<iostream>
 2 #include<cstdio>
 3 #include<cstring>
 4 #include<algorithm>
 5 using namespace std;
 6 typedef long long ll;
 7 /*注意数据范围*/
 8 const int MAXN=10010;
 9 ll n;
10 ll factor[MAXN];
11  
12 void get_factor()
13 /*必须在n^(1/2)时间以内求出所有的质因数，否则会TE*/
14 {
15     memset(factor,0,sizeof(factor));
16     ll i;
17     for (i=1;i*i<n;i++)
18     {
19         if (n%i==0)
20         {
21             factor[++factor[0]]=i;
22             factor[++factor[0]]=n/i;
23         }
24     }
25     if (i*i==n) factor[++factor[0]]=i;
26 }
27  
28 ll eular(ll k)
29 {
30     ll res=k;
31     for (ll p=2;p*p<=k;p++)
32     {
33         if (k%p==0)
34         {
35             res=res-res/p;
36             while (k%p==0) k/=p;
37         }
38     }
39     if (k>1) res=res-res/k;
40     /*主意k可能大于0，必须要再减去*/
41     return res;
42 }
43  
44 void init()
45 {
46     scanf("%d",&n);
47 }
48  
49 ll get_ans()
50 {
51     ll result=0;
52     for (ll i=1;i<=factor[0];i++)
53         result+=eular(n/factor[i])*factor[i];
54     return result;
55 }
56  
57 int main()
58 {
59     init();
60     get_factor();
61     cout<<get_ans()<<endl;
62     return 0;
63 }