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 <bits/stdc++.h>
#define ll long long
#define SZ(vvv) ((int)vvv.size())
#define fastIO cout << fixed << setprecision(12), ios::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr)
using namespace std;

const int N = 5e5 + 5, M = 5e4 + 9, INF = 1e9, MOD = 1e9 + 7;

void runtestcase() {
	int n;
	cin >> n;
	ll ans = 0;
	for (int i = 1; i < n; ++i) {
		int rem = n - i;
		for (int j = 1; 1ll * j * j <= rem; ++j) {
			if(rem % j == 0) {
				int k = rem / j;
				++ans;
				if(k != j) ++ans;
			}
		}
	}
	cout << ans;
}


int main() {
    fastIO;
#ifdef LOCAL
    freopen("input.in", "rt", stdin);
//    freopen("cache.out", "wt", stdout);
#endif
  int t = 1, tt = 1;
//	cin >> t;
  while(t) {
//		cout << "Case #" << tt << ':' << ' ';
    runtestcase();
    if(t)
    	cout << '\n';
    --t, ++tt;
  }
}