p4980 polya定理

传送门

分析

orz ymh

代码

#include<iostream>
#include<cstdio>
#include<cstring>
#include<string>
#include<algorithm>
#include<cctype>
#include<cmath>
#include<cstdlib>
#include<ctime>
#include<queue>
#include<vector>
#include<set>
#include<map>
#include<stack>
using namespace std;
#define int long long
const int mod = 1e9+;
inline int pw(int x,int p){
    int res=;
    while(p){
      if(p&)res=res*x%mod;
      x=x*x%mod;
      p>>=;
    }
    return res;
}
inline int phi(int x){
    int res=x;
    for(int i=;i*i<=x;i++)
      if(x%i==){
          res=res/i*(i-);
          while(x%i==)x/=i;
      }
    if(x>)res=res/x*(x-);
    return res;
}
signed main(){
    int t,n,m,i,j,k,Ans;
    scanf("%d",&t);
    while(t--){
      scanf("%d",&n);
      Ans=;
      for(i=;i*i<=n;i++)
        if(n%i==){
            Ans=(Ans+pw(n,i)*phi(n/i)%mod)%mod;
            if(i*i!=n)Ans=(Ans+pw(n,n/i)*phi(i)%mod)%mod;
        }
      cout<<Ans*pw(n,mod-)%mod<<endl;
    }
    return ;
}