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: Time Limit Exceeded)

require 'prime'
n = gets.to_i

ans = 1

if n == 2
  puts ans
  exit
end

2.upto(n-1) do |i|
  prime_division = Prime.prime_division(i)
  count = 1
  prime_division.each do |p, e|
    count *= e + 1
  end
  ans += count
end

puts ans