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 <iomanip>
#include <vector>
#include <algorithm>
#include <numeric>
#include <functional>
#include <cmath>
#include <queue>
#include <stack>
#include <string>
#include <cmath>
#include <limits>
#include <math.h>
#include <cassert>
#include <map>
#define REP(i, n) for (int i = 0; i < n; i++)
#define REPR(i, n) for (int i = n; i >= 0; i--)
#define FOR(i, m, n) for (int i = m; i < n; i++)
#define INF 1000000007
#define ALL(v) v.begin(), v.end()
using namespace std;
typedef long long ll;

int prime_factor(int a)
{
    int ans = 1;
    for (int i = 2; i <= sqrt(a); i++)
    {
        int cnt = 0;
        while (a % i == 0)
        {
            cnt++;
            a /= i;
        }
        ans *= (cnt + 1);
        if (a == 1)
            break;
    }
    if (a != 1)
        ans *= 2;
    return ans;
}

int main()
{
    int N;
    cin >> N;
    int c = 1;
    for (int i = 2; i < N; i++)
    {
        c += prime_factor(i);
    }
    cout << c << endl;
}