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.to_i
pre_sieve = Array.new(n) { |i| i }
sieve = Array.new(n)
ans = 0

s = Math.sqrt(n - 1).to_i
2.upto(s) do |i|
  ((n - 1) / i).times do |j|
    pre_sieve[i * (j + 1)] = i if i < pre_sieve[i * (j + 1)]
  end
end

2.upto(n - 1) do |i|
  h = Hash.new(0)
  x = i
  while x != 1
    h[pre_sieve[x]] += 1
    x /= pre_sieve[x]
  end
  sieve[i] = h
end

2.upto(n - 1) do |i|
  x = 1
  sieve[i].each_value do |j|
    x *= (j + 1)
  end

  ans += x
end

puts ans + 1