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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int count = 0;
        for (int c=1; c<=n-1; c++) {
            count += di(n-c);
        }
        System.out.print(count);
    }

    static int di(int ab) {
        int k = 1;
        for (int i=2; i<=ab; i++) {
            if (ab % i != 0) continue;
            int c = 0;
            while ((ab % i) == 0) {
                ab = ab / i;
                c += 1;
            }
            k *= c + 1;
        }
        return k;
    }
}