Problem:
Score : 300 points

Problem Statement

Given is a positive integer N.
How many tuples (A,B,C) of positive integers satisfy A \times B + C = N?

Constraints

2 \leq N \leq 10^6

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N

Output

Print the answer.

Sample Input 1

3

Sample Output 1

3

There are 3 tuples of integers that satisfy A \times B + C = 3: (A, B, C) = (1, 1, 2), (1, 2, 1), (2, 1, 1).

Sample Input 2

100

Sample Output 2

473

Sample Input 3

1000000

Sample Output 3

13969985

Solution in C++ (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

#include <iostream>
#include <math.h>
#include <algorithm>
#include <string>
#include <vector>
using namespace std;

long int divisor(long long n,vector<long long> ret) {
    
    long int siz;
    for (long long i = 1; i * i <= n; i++) {
        if (n % i == 0) {
            ret.push_back(i);
            if (i * i != n) ret.push_back(n / i);
        }
    }
    
    siz = ret.size();
    return siz;
}

int main(){
  long int i,n,cnt=0;
  vector<long long> ret;

  cin >> n;
  
  for ( i = 1; i < n; i++)
  {
    cnt = cnt + divisor(n-i ,ret);
    ret.clear();
  }

  cout << cnt;
  
  
  return 0;
}