hdu 1787 GCD Again

GCD Again

Time Limit: 1000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 2838    Accepted Submission(s): 1214

Problem Description

Do you have spent some time to think and try to solve those unsolved problem after one ACM contest?
No? Oh, you must do this when you want to become a "Big Cattle".
Now you will find that this problem is so familiar:
The greatest common divisor GCD (a, b) of two positive integers a and b, sometimes written (a, b), is the largest divisor common to a and b. For example, (1, 2) =1, (12, 18) =6. (a, b) can be easily found by the Euclidean algorithm. Now I am considering a little more difficult problem:
Given an integer N, please count the number of the integers M (0<M<N) which satisfies (N,M)>1.
This is a simple version of problem “GCD” which you have done in a contest recently,so I name this problem “GCD Again”.If you cannot solve it still,please take a good think about your method of study.
Good Luck!

 

Input

Input contains multiple test cases. Each test case contains an integers N (1<N<100000000). A test case containing 0 terminates the input and this test case is not to be processed.

 

Output

For each integers N you should output the number of integers M in one line, and with one line of output for each line in input.

 

Sample Input

240

 

Sample Output

01

 

Author

lcy

 

Source

2007省赛集训队练习赛（10）_以此感谢DOOMIII

 

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题目大意：给出一个数n，求1到n-1 中与n不互质的数的个数

题解：sqrt(n) 求phi , 通式phi(n)=n*(1-1/p₁)(1-1/p₂)..(1-1/p_n)，p₁,p₂..p_n为n的所有质因数。每个括号都可以化成（pi-1)/pi的形式，然后搞一搞就可以了。

#include<iostream>#include<cstdio>#include<cstring>#include<cmath>using namespace std;long long n,x;long long phi(long long k){  long long sum=k;  for (int i=2;i*i<=k;i++)   if (k%i==0)   {    sum=sum*(i-1)/i;    while (k%i==0)     k/=i;   }  if (k>1)  sum=sum*(k-1)/k;  return sum;}int main(){  scanf("%I64d",&n);  while (n)   {    printf("%I64d\n",n-1-phi(n));    scanf("%I64d",&n);   }}