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 Ruby (2.7.1) (judge verdict: Accepted)

N = gets.chomp.to_i

require 'complex'
root = Math.sqrt(N-1).floor
ans = 0

if N == 2
  puts 1
  exit
end

(1..root).each do |i|
  ans += ((N-1) / i)
  if N / i != i
    ans +=( ((N-1)/i) - ((N-1)/(i+1)))*i
  end
end

puts ans