Perfect P-th Powers UVA

将得到的数进行分解，也就是找出该素数所有的素因子以及素因子对应的指数，那么问题也就转化成求解这些素因子的最大公约数。素数可以打表得到，另外需要注意输入的数据为1的情况也就是对应的下边的代码中ans为0的情况，同时要注意处理输入的数据是负数的情况，具体实现见如下代码：

#include<iostream>#include<vector>#include<string>#include<set>#include<stack>#include<queue>#include<map>#include<algorithm>#include<cmath>#include<iomanip>#include<cstring>#include<sstream>#include<cstdio>#include<deque>#include<functional>using namespace std;const int maxn = 600000;int vis[maxn + 5];vector<int> prime;void Init(){memset(vis,0,sizeof(vis));vis[0] = vis[1] = 1;int up = floor(sqrt(maxn) + 0.5);for (int i = 2; i <= up; i++){if (!vis[i]){for (long long j = i*i; j <= maxn; j += i)vis[j] = 1;}}for (int i = 2; i <= maxn; i++)if(!vis[i]) prime.push_back(i);}int gcd(int a, int b){if (!b) return a;return gcd(b, a%b);}long long N;int main(){Init();while (cin >> N){bool flag = false;if (N < 0){N = -N;flag = true;}if (N == 0) break;int ans = 0;int n = prime.size();for (int i = 0; i < n && prime[i] <= N; i++){int amount = 0;if (N%prime[i] == 0){while (N%prime[i]==0){N = N/prime[i];amount++;}}ans = gcd(ans,amount);}if (ans == 0) ans = 1;if (flag){while (ans % 2 == 0)ans = ans / 2;}cout << ans << endl;}return 0;}