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<cmath>
int main(){
	
	std::uint32_t n;
	std::cin >> n;


	std::uint64_t ans_{};

	for( std::uint32_t ci{ 1 }; ci < n; ++ci ) {
		const auto ab_ = n - ci;
		std::uint32_t max_ = std::sqrt( ab_ );
		for( std::uint32_t ai{ 1 }; ai <= max_; ++ai )
		{
			if( ab_ % ai != 0 )
				continue;

			ans_ += ab_ / ai == ai ? 1 : 2;
		}
	}
	std::cout << ans_ << "\n";
	return 0; 
}