欧拉函数and Relatives ac

欧拉函数φ(N)表示小于或等于N的正整数中与N互质的数的个数。又称φ函数、欧拉商数。

下面介绍欧拉函数的几个性质：

我们根据这几个性质就可以求出欧拉函数。

基本思路是首先置φ(N)=N，然后再枚举素数p，将p的整数倍的欧拉函数φ(kp)进行如下操作。

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例题

Given n, a positive integer, how many positive integers less than n are relatively prime to n? Two integers a and b are relatively prime if there are no integers x > 1, y > 0, z > 0 such that a = xy and b = xz.

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Input

There are several test cases. For each test case, standard input contains a line with n <= 1,000,000,000. A line containing 0 follows the last case.

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Output

For each test case there should be single line of output answering the question posed above.

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Sample Input

7
12
0

Sample Output

6
4

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#include<iostream>
#include<cstdio>
typedef long long ll;
using namespace std;
ll f(ll a){
	ll ans=1;
	for(int i=2;i*i<=a;i++){
		if(a%i==0){
			a/=i;ans*=i-1;
	        while(a%i==0){    //用来求幂
	        	a/=i;ans*=i;
			}
		}
	}
	if(a>1) ans*=a-1;    //如果本身是质数那么质数-1就是结果 
	return ans;
} 
int main()
{
	ll n;
	while(cin>>n){
		if(n==0) break;
		cout<<f(n)<<endl;
	}
	return 0;
}