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 Rust (1.42.0) (judge verdict: Time Limit Exceeded)

use whiteread::parse_line;

fn divisors(n: usize) -> Vec<usize> {
    let mut divisors = Vec::new();
    for i in 1..=(f64::sqrt(n as f64) + 1e-9) as usize {
        if n % i == 0 {
            divisors.push(i);
            if i != n / i {
                divisors.push(n / i);
            }
        }
    }
    divisors.sort();
    return divisors;
}

fn main() {
    let n: usize = parse_line().unwrap();
    let mut t: usize = 0;
    let (mut a, mut c): (usize, usize) = (1, 1);
    while c < n {
        let k: usize = n - c;
        let v = divisors(k);
        t = t + v.len();
        c = c + 1;
    }
    println!("{}", t);
}