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 OCaml (4.10.0) (judge verdict: Time Limit Exceeded)

open Printf
open Scanf

let input_int () =
  scanf "%d\n" (fun k -> k)

let g n =
  let m = int_of_float (sqrt (float_of_int n)) in
  let rec loop count k =
    if k>m then
      if m * m = n then
        2 * count - 1
      else
        2 * count
    else if n mod k = 0 then
      loop (count+1) (k+1)
    else
      loop count (k+1)
  in
  loop 0 1

let f () =
  let n = input_int () in
  let rec loop tot c =
    if c = n then
      tot
    else
      loop (tot + g (n - c)) (c+1)
  in
  loop 0 1

let () =
  let tot = f () in
  printf "%d\n" tot