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++ (Clang 10.0.0) (judge verdict: Accepted)

#include <iostream>
#include <vector>
using namespace std;

vector<pair<long long, long long>> prime_factorize(long long N)
{
    vector<pair<long long, long long>> res;
    for (long long a = 2; a * a <= N; ++a)
    {
        if (N % a != 0)
            continue;
        long long ex = 0;
        while (N % a == 0)
        {
            ++ex;
            N /= a;
        }
        res.push_back({a, ex});
    }
    if (N != 1)
        res.push_back({N, 1});
    return res;
}

int main()
{
    long long N, cnt = 0;
    cin >> N;
    for (long long C = 1; C < N; ++C)
    {
        const auto &pf = prime_factorize(N - C);
        long long res = 1;
        for (auto p : pf)
            res *= p.second + 1;
        cnt += res;
    }
    cout << cnt << endl;
}