【poj 2407】 Relatives 【Waterloo local 2002.07.01】

Description

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

这道题的题意是求与n互质的小于n的数的个数，即求欧拉函数，下面是程序：

#include<stdio.h>
#include<iostream>
using namespace std;
int read(){
	int s=0;
	char c=getchar();
	while(c<'0'||c>'9'){
		c=getchar();
	}
	while(c>='0'&&c<='9'){
		s*=10;
		s+=c-'0';
		c=getchar();
	}
	return s;
}
int work(int n){
	int s=n,i=2;
	while(i*i<=n){
		if(!(n%i)){
			s=s/i*(i-1);
			while(!(n%i)){
				n/=i;
			}
		}
		i++;
	}
	if(n>1){
		s=s/n*(n-1);
	}
	return s;
}
int main(){
	int n;
	while(n=read()){
		printf("%d\n",work(n));
	}
	return 0;
}