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 fast ios_base::sync_with_stdio(0);cin.tie(NULL);cout.tie(NULL)
#define ll long long int
#define ld long double
using namespace std;
const int N = 1e6 + 1;
const int MOD = 1e9 + 7;
vector<ll> factors[N];

void sieve(){
	for(int i = 1; i < N; ++i)
		for(int j = i; j < N; j += i)
			factors[j].push_back(i);
}

int main(){
	fast;
	ll n, ans = 0;
	cin >> n;
	sieve();
	for(int i = 1; i < n; ++i){
		ll x = n - i;
		ans += factors[x].size();
	}
	cout << ans;
  	cerr << "Time elapsed : " << 1.0 * clock() / CLOCKS_PER_SEC << " sec \n";
	return 0;
}