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 <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <map>
#include <queue>
#include <functional>
#include <vector>
#include <stack>
#include <set>
#include <bitset>
using namespace std;
typedef  long long ll;
const int maxn=2e5+50;
const int inf=0x3f3f3f3f;
const int MOD=1e9+7;
const int HASH=131;

int cnt(int x)
{
    int ans=1;
    for(int i=2;i*i<=x;i++)
    {
        if(x%i==0)
        {
            int tmp=0;
            while(x%i==0)
            {
                x/=i;
                tmp++;
            }
            ans*=(tmp+1);
        }
    }
    if(x>1) ans*=2;
    return ans;
}


int main()
{
    int n;
    cin>>n;
    int sum=0;
    for(int i=1;i<n;i++)
    {
        int ans=n-i;
        sum+=cnt(ans);
    }
    cout<<sum<<endl;
    return 0;
}