FOJ 1012 Relatives(欧拉值)

Problem 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 integersx > 1, y > 0, z > 0 such that a = xy and b = xz.

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

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

Sample Input

7120

Sample Output

64

这道题就是求比一个数小又和这个数互质的个数，就是欧拉值，这是前人已经推导出来了；

phi=n/(P1)*(P1-1)/P2*(P2-1)....../(Pn-1)*(Pn-1 - 1)/Pn*(Pn - 1),带公式就行；P是素因子

AC代码：

# include <stdio.h> # include <math.h># include <stdlib.h>int euler_phi(int n){int m=sqrt(n+0.5);int ans=n;for(int i=2; i<=m; i++){if(n%i==0){ans=ans/i*(i-1);}while(n%i==0){n=n/i;}}if(n>1)ans=ans/n*(n-1);return ans;}int main(){int n;while(scanf("%d", &n)){if(n==0){break;}printf("%d\n", euler_phi(n));}return 0;}