bzoj2705 [SDOI2012]Longge的问题

Posted 2020-12-25 hehe54321

https://www.lydsy.com/JudgeOnline/problem.php?id=2705

先化简。。

化简出来，这个函数就是$id*id*mu=id*varphi$

可以暴力枚举n的因子求。。

 1 #include<cstdio>
 2 #include<algorithm>
 3 #include<cstring>
 4 #include<vector>
 5 using namespace std;
 6 #define fi first
 7 #define se second
 8 #define mp make_pair
 9 #define pb push_back
10 typedef long long ll;
11 typedef unsigned long long ull;
12 typedef pair<int,int> pii;
13 bool nprime[100100];
14 ll prime[30100],len;
15 ll phi(ll x)
16 {
17     ll i,ans=x;
18     for(i=1;prime[i]*prime[i]<=x;i++)
19         if(x%prime[i]==0)
20         {
21             ans=ans/prime[i]*(prime[i]-1);
22             while(x%prime[i]==0)    x/=prime[i];
23         }
24     if(x>1)    ans=ans/x*(x-1);
25     return ans;
26 }
27 int main()
28 {
29     ll i,j;
30     nprime[1]=1;
31     for(i=2;i<=100000;i++)
32     {
33         if(!nprime[i])    prime[++len]=i;
34         for(j=1;j<=len&&i*prime[j]<=100000;j++)
35         {
36             nprime[i*prime[j]]=1;
37             if(i%prime[j]==0)    break;
38         }
39     }
40     ll n,ans=0;
41     scanf("%lld",&n);
42     for(i=1;i*i<=n;i++)
43         if(n%i==0)
44         {
45             ans+=i*phi(n/i);
46             if(n/i!=i)
47                 ans+=(n/i)*phi(i);
48         }
49     printf("%lld",ans);
50     return 0;
51 }