Luogu4980 【模板】Polya定理（Polya定理+欧拉函数）

#include<iostream> 
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
#define ll long long
#define P 1000000007
#define N 100
char getc(){char c=getchar();while ((c<‘A‘||c>‘Z‘)&&(c<‘a‘||c>‘z‘)&&(c<‘0‘||c>‘9‘)) c=getchar();return c;}
int gcd(int n,int m){return m==0?n:gcd(m,n%m);}
int read()
{
    int x=0,f=1;char c=getchar();
    while (c<‘0‘||c>‘9‘) {if (c==‘-‘) f=-1;c=getchar();}
    while (c>=‘0‘&&c<=‘9‘) x=(x<<1)+(x<<3)+(c^48),c=getchar();
    return x*f;
}
int m,T,prime[N],cnt[N],p[N][N],t,ans;
int ksm(int a,int k)
{
    int s=1;
    for (;k;k>>=1,a=1ll*a*a%P) if (k&1) s=1ll*s*a%P;
    return s;
}
void dfs(int k,int s,int phi)
{
    if (k>t) {ans=(ans+1ll*ksm(m,s-1)*phi)%P;return;}
    for (int i=0;i<cnt[k];i++) dfs(k+1,1ll*s*p[k][i]%P,1ll*phi*(prime[k]-1)%P*p[k][cnt[k]-i-1]%P);
    dfs(k+1,1ll*s*p[k][cnt[k]]%P,phi);
}
int main()
{
#ifndef ONLINE_JUDGE
    freopen("a.in","r",stdin);
    freopen("a.out","w",stdout);
    const char LL[]="%I64d\n";
#else
    const char LL[]="%lld\n";
#endif
    T=read();
    while (T--)
    {
        int n=read();m=n,t=0;
        for (int i=2;i*i<=n;i++)
        if (n%i==0)
        {
            prime[++t]=i,cnt[t]=1;n/=i;
            while (n%i==0) cnt[t]++,n/=i;
        }
        if (n>1) prime[++t]=n,cnt[t]=1;
        for (int i=1;i<=t;i++)
        {
            p[i][0]=1;
            for (int j=1;j<=cnt[i];j++) p[i][j]=1ll*p[i][j-1]*prime[i]%P;
        }
        ans=0;dfs(1,1,1);
        printf("%d\n",ans);
    }
    return 0;
}