Gym 100917C Constant Ratio 数论+暴力

题目：

Description

standard input/output
Statements

Given an integer n, find out number of ways to represent it as the sum of two or more integers a_i with the next property: ratio a_i / a_i - 1is the same positive integer for all possible i > 1.

Input

Input consists of one integer n (1 ≤ n ≤ 10⁵).

Output

Print one integer — number of representations.

Sample Input

Input

1

Output

0

Input

5

Output

2

Input

567

Output

21

Hint

In the first sample no such representation exists.

In the second sample there exist two representations:

• 1 1 1 1 1, then q = 1.
• 1 4, then q = 4.

题目大意：给出一个等比数列（至少连个元素）的和n，要求公比q为整数，求满足要求的等比数列的个数。

题目思路：Sn=a1*(1-q^n)/(1-q),枚举q的值，判断a1是否为整数，比较暴力……

 #include<iostream>
 #include<algorithm>
 #include<cstring>
 #include<vector>
 #include<stdio.h>
 #include<stdlib.h>
 #include<queue>
 #include<math.h>
 #define INF 0x3f3f3f3f
 #define MAX 1000005
 #define Temp 1000000000

 using namespace std;

 int check(long long q,long long n)
 {
     long long a=q;
     int ans=;
     while(n*(q-)/(a-) >= )
     {
         if(n*(q-)%(a-)== && n*(q-)/(a-)>= && n*(q-)/(a-)<n)//判断a1是否为整数，且满足要求
             ans++;
         a*=q;
     }
     return ans;
 }

 int main()
 {
     int n,sum;
     sum=;
     scanf("%d",&n);
     for(int i=; i<n; i++)
     {
         if(n%i== && n/i>)
             sum++;
     }
     for(int i=; i<n; i++)//枚举公比的值
     {
         sum+=check(i,n);
     }
     printf("%d\n",sum);
     return ;
 }