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: Accepted)

#include <iostream>
#include <math.h>
using namespace std;
int main(){
    int N;
    cin >> N;
    int count = 0;
    int A;
    int B;
    int AB;
    int C;
    int sqrtAB;
    for(C=1; C<N; C++){
        AB = N-C;
        if(AB==1){
            count++;
            continue;
        }
        sqrtAB = ceil(sqrt(AB));
        if(pow(sqrtAB, 2)==AB){
            sqrtAB += 1;
        }
        for(B=1; B<sqrtAB; B++){
            if(AB%B!=0){
                continue;
            }
            A = AB/B;
            if(A==B){
                count++;
                continue;
            }
            count += 2;
        }   
    }
    cout << count << endl;
    return 0;
}