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: Accepted)

Scanf.scanf "%d" (fun n ->
    let rec loop_a a acc =
        let rec loop_b b acc =
            if a * b >= n then loop_a (a + 1) acc else
                loop_b (b + 1) (acc + 1)
        in
        if a >= n then acc else loop_b 1 acc
    in
    loop_a 1 0 |> Printf.printf "%d\n"
)