[數論] HOJ 1953 Relatives 歐拉函數

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Relatives

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	Source : Waterloo ACM Programming Contest June 1, 2002
	Time limit : 1 sec		Memory limit : 32 M

Submitted : 536, Accepted : 226

""""

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.

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.

Output

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

Sample Input

7
12
0

Sample Output

6
4

解題報告：

此題爲歐拉函數模板題，代碼如下：

#include<iostream>
#include<cstdio>
using namespace std;
int eular(int n){
	int ret=1,i;
	for(i=2;i*i<=n;i++)
		if (n%i==0){
			n/=i,ret*=i-1;
			while (n%i==0)
				n/=i,ret*=i;
		}
		if (n>1)
			ret*=n-1;
		return ret;    //n的歐拉數
}
int main(){
    int n;
    while(scanf("%d",&n)&&n){
        printf("%d\n",eular(n));
    }
    return 0;
}