Relatives 【POJ - 2407】【欧拉筛、预处理】

最新推荐文章于 2019-05-07 12:18:00 发布

Wuliwuliii

最新推荐文章于 2019-05-07 12:18:00 发布

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分类专栏：数论文章标签：欧拉公式

本文链接：https://blog.youkuaiyun.com/qq_41730082/article/details/81452725

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本文介绍了一种计算小于给定正整数n并与n互质的正整数数量的方法。通过解析输入并利用数学原理，文章提供了一个有效的算法实现。

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

#include <iostream>
#include <cstdio>
#include <cmath>
#include <string>
#include <cstring>
#include <algorithm>
#include <limits>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#define lowbit(x) ( x&(-x) )
using namespace std;
typedef long long ll;
ll N;
ll oula(ll n)
{
    ll res=n;
    for(ll i=2; i*i<=n; i++)
    {
        if(n%i==0)
        {
            res=res/i*(i-1);
            while(n%i==0) n/=i;
        }
    }
    if(n>1) res=res/n*(n-1);
    return res;
}
int main()
{
    while(scanf("%lld",&N)&&N)
    {
        printf("%lld\n",oula(N));
    }
    return 0;
}