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>

using namespace std;

int divisor(int n) {
    int res = 0;
    for (long long i = 1; i * i <= n; ++i) {
        if (n % i == 0) {
            ++res;
            if (i * i != n) ++res;
        }
    }
    return res;
}

int main() {
	int n; cin >> n;
    long long ans = 0;
	for (int c = 1; c < n; ++c) {
		int t = n - c;
        ans += divisor(t);
	}
    cout << ans << endl;

	return 0;
}