HDU-3501: Calculation 2（欧拉函数）

数论

Description

Given a positive integer N, your task is to calculate the sum of the positive integers less than N which are not coprime to N. A is said to be coprime to B if A, B share no common positive divisors except 1.

Input

For each test case, there is a line containing a positive integer N(1 ≤ N ≤ 1000000000). A line containing a single 0 follows the last test case.

Output

For each test case, you should print the sum module 1000000007 in a line.

Sample Input

3
4
0

Sample Output

0
2

题意：求小于n并且与n不互质的数的和。

分析：欧拉函数求出phi（n），小于n并且与n互质的数的和为：n*phi（n）/2。小于n的所有数的和减去与n互质的数的和。

• 完整代码：

#include<stdio.h>
#include<math.h>
#define LL long long 
#define MOD 1000000007
LL phi(LL n)
{
    //LL m=(LL)sqrt(n+0.5) //开方很慢，265ms
    LL ans=n;
    for(LL i=2;i*i<=n;i++) //写成i*i<=n而不是i<=m，15ms
        if(n%i==0)
    {
        ans=ans/i*(i-1);
        while(n%i==0)
            n/=i;
    }
    if(n>1)
        ans=ans/n*(n-1);
    return ans;
}
int main()
{
    LL n;
    while(scanf("%lld",&n),n)
    {
     //   n*phi(n)/2 小于n且与n互质的数的和
        printf("%lld\n",(n*(n-1)/2-n*phi(n)/2)%MOD);
    }
    return 0;
}