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 Scala (2.13.1) (judge verdict: Accepted)

import scala.annotation.tailrec

object Main extends App {
  val sc = new java.util.Scanner(System.in)
  val n = sc.nextInt

  val i1 = (1 to Math.sqrt(n).toInt).map(i => loopJ(i, i + 1, 0)).sum
  val i2 = loopI(1, 0)
  //println(i1)
  //println(i2)
  println(i1 * 2 + i2)

  @tailrec
  def loopJ(i: Int, j: Int, count: Int): Int = {
    if (i * j < n) {
      //println(i + " " + j)
      loopJ(i, j + 1, count + 1)
    } else {
      count
    }
  }

  @tailrec
  def loopI(i: Int, count: Int): Int = {
    if (i * i < n) {
      //println(i + " " + i)
      loopI(i + 1, count + 1)
    } else {
      count
    }
  }

}