Relatives
| Time Limit: 1000MS | Memory Limit: 65536K | |
| Total Submissions: 15566 | Accepted: 7900 |
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
Source
题目大意
给定$n$，求出$\varphi \left( n\right)$
直接套公式。
$\varphi \left( n\right) =n\prod ^{k}_{i=1}\left( \dfrac {p_{i}-1}{p_{i}}\right)$
注意先除再乘，否则会爆精度
#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#define LL long long
using namespace std;
int main()
{
LL N;
while(cin>>N&&N!=)
{
int limit=sqrt(N),ans=N;
for(int i = ; i <= limit ; ++i)
{
if(N%i==) ans=ans/i*(i-);
while(N%i==) N=N/i;
}
if(N>) ans=ans/N*(N-);
printf("%d\n",ans);
}
return ;
}