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: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
bool prime(int n)
{
	int flag=0;
	if(n==2 || n==3)
	return 1;
	for(int i=2;i<=sqrt(n);i++)
	{
		if(n%i==0)
		{
			flag++;
			break;
		}
	}
	if(flag==0)
	return 1;
	else
	return 0;
}
int main()
{
	int n;
	cin>>n;
	int prim[100000];
	int it=0;
	for(int i=2;i<=1000000;i++)
	{
		if(prime(i)){
			prim[it]=i;
			it++;
		}
	}
	int tmp=0;
	int no_factors=1;
	int count=0;
	for(int i=1;i<n;i++)
	{
		int x=n-i;
		no_factors=1;
		if(binary_search(prim,prim+it,x))
		{
			//cout<<"fwf\n";
			count=count+2;
		}
		else
		{
			//cout<<"Qeqfer\n";
			int c=0;
			if(x==1)
			{
				count++;
				break;
			}
			for(int j=prim[tmp];j<it;)
			{
				if(x==1)
				break;
				if(x%prim[j]==0)
				{
					c++;
					x=x/prim[j];
				}
				else
				{
					no_factors*=c+1;
					c=0;
					j++;
				}
			}
			count+=no_factors;
		}
		//cout<<count<<"\n";
	}
	cout<<count<<"\n";
}