Necklace of Beads （polya定理的引用）

#include<iostream>
#include<cmath>

using namespace std;
#define ll long long

ll Pow(int value,int num)
{   __int64 sum=1;
    for(int i=1;i<=num;i++)
        sum*=value;
    return sum;
}

int gcd(int a, int b)
{
    if(b) return gcd(b, a%b);
    else return a;
}

ll polya(int col, int num)  // col 表示颜色种类， num 表示换环的长度
{
    ll sum = 0;
    for(int i = 1; i <= num; i++)
    {
        sum += Pow(col, gcd(num,i));
    }
    if(num&1) sum += num*(Pow(col, num/2+1));
    else sum += (Pow(col, num/2) + Pow(col, num/2+1))*(num/2);
    return sum/2/num;

}

int main()
{
    int n;
    while(cin >> n, n != -1)
    {
        if(n == 0) cout << 0 << endl;
        else
        {
            ll ans = polya(3,n);
            cout << ans << endl;
        }

    }
    return 0;
}