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: Accepted)

use proconio::input;

fn main() {
    input! {
        n: usize,
    };

    let mut spf = vec![0; n + 1];
    for i in 0..n + 1 {
        spf[i] = i;
    }
    for p in 2.. {
        if p * p > n {
            break;
        }
        for i in (p..n + 1).step_by(p) {
            if spf[i] == i {
                spf[i] = p;
            }
        }
    }

    let mut ans = 0_usize;
    for i in 1..=n - 1 {
        let mut x = i;
        let mut map = std::collections::BTreeMap::new();
        while x != 1 {
            let p = spf[x];
            *map.entry(p).or_insert(0) += 1;
            x /= p;
        }

        let mut c = 1;
        for (_, v) in map {
            c *= v + 1;
        }
        ans += c;
    }
    println!("{}", ans);
}