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=0;
    while(n*(q-1)/(a-1) >= 1)
    {
        if(n*(q-1)%(a-1)==0 && n*(q-1)/(a-1)>=1 && n*(q-1)/(a-1)<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=0;
    scanf("%d",&n);
    for(int i=1; i<n; i++)
    {
        if(n%i==0 && n/i>1)
            sum++;
    }
    for(int i=2; i<n; i++)//枚举公比的值
    {
        sum+=check(i,n);
    }
    printf("%d
",sum);
    return 0;
}