【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

7120

Sample Output

64

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;}