模板题,无题解。
Code:
#include<bits/stdc++.h>
#define rep(i,j,k) for(int i=j;i<=k;i++)
#define mo 1000000007
using namespace std;
int len=0;
int prime[100010];bool f[100010];
inline void ols(){
rep(i,2,100000){
if(!f[i]){prime[++len]=i;}
rep(j,1,len){
if(prime[j]*i>100000)break;
f[prime[j]*i]=1;
if(i%prime[j]==0)break;
}
}
}
inline int olhs(int x){
int ret=x;int temp=x;
rep(i,1,len){
if(1ll*prime[i]*prime[i]>1ll*temp)break;
if(temp%prime[i])continue;
while(!(temp%prime[i]))temp/=prime[i];
ret/=prime[i];ret*=(prime[i]-1);
}
if(temp>1){ret/=temp;ret*=(temp-1);}
return ret;
}
inline int poww(int n,int m){
int re_value=1;int temp=n;int tmp=m;
while(tmp){
if(tmp&1)re_value=(1ll*re_value*temp)%mo;
temp=(1ll*temp*temp)%mo;
tmp>>=1;
}
return re_value;
}
int main(){
int T;scanf("%d",&T);
ols();
while(T--){
int n;scanf("%d",&n);
long long ans=0;
rep(i,1,n){
if(1ll*i*i>1ll*n)break;
if(n%i)continue;
long long temp=1ll*olhs(i)*poww(n,n/i-1);
temp%=mo;
ans+=temp;ans%=mo;
if(i*i!=n){
temp=1ll*olhs(n/i)*poww(n,i-1);
temp%=mo;ans+=temp;ans%=mo;
}
}
printf("%lld\n",ans);
}
return 0;
}