92-珠子染色-置换群

#include <iostream>
#include <algorithm>
#include <cmath> 
using namespace std;
#define LL long long

LL gcd(LL a, LL b){
	return b == 0 ? a : gcd(b, a % b);
}

int main(){
	LL n, sum = 0;
	while(cin >> n && n != -1){
		if(n == 0){
			cout << 0 << endl;
			continue;
		}
		//旋转变换 
		//n种置换，步长为x的置换的循环节有GCD(x,n)个
		for(int i = 1; i <= n; i++){
			sum += pow(3, gcd(i, n));
		}
		//翻转变换：要分奇偶
		if(n & 1){
			sum += n * pow(3, (n - 1) / 2 + 1);
		} 
		else{
			sum += n/2 * pow(3, (n - 2) / 2 + 2); //按两个点翻转 
			sum += n/2 * pow(3, n / 2); //按边翻转   
		}
		sum /= 2 * n;  //除以G：总的置换个数 
		cout << sum << endl; 
		sum = 0; 
	}
}