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<bits/stdc++.h>

using namespace std;

int main(){
    int n;

    cin>>n;

    vector<int> ways_represent(n+1);
    ways_represent[1]=1;
    ways_represent[2]=2;

    for(int i=3; i<n; i++){
        int a, b;
        ways_represent[i]=0;
        for(int j=1; j<=sqrt(i); j++){
            a=j;
            if(i%j > 0){
                continue;
            }

            b=i/j;
            if(a==b){
                ways_represent[i]+=1;
            }
            else{
                ways_represent[i]+=2;
            }

        }
    }

    long long int ans=0;

    for(int i=1; i<n; i++){
        ans+=ways_represent[i];
    }

    cout<<ans<<'\n';

    return 0;
}