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)

#[allow(unused_imports)]
use proconio::marker::{Bytes, Chars, Usize1};
use proconio::{fastout, input};
use std::collections::HashMap;
#[fastout]
fn main() {
    input! {
        n: usize,
    }
    let mut ans = 0;
    for i in 1..n {
        let prime = trial_division(n - i);
        let mut count = 1;
        for (_, value) in prime.iter() {
            count *= value + 1;
        }
        ans += count;
    }
    println!("{}", ans);
}

fn trial_division(mut n: usize) -> HashMap<usize, usize> {
    let mut primes = HashMap::new();
    let mut i = 2;

    //  n を root n 以下の整数で割り切れるまで割っていく
    while i * i <= n {
        while n % i == 0 {
            n /= i;
            if primes.contains_key(&i) {
                let x = primes.get_mut(&i).unwrap();
                *x += 1;
            } else {
                primes.insert(i, 1);
            }
        }
        i += 1;
    }

    // 最後にnが素数になっている場合はそれ自身も素因数に含めて終了
    if n > 1 {
        if primes.contains_key(&n) {
            let x = primes.get_mut(&n).unwrap();
            *x += 1;
        } else {
            primes.insert(n, 1);
        }
    }
    primes
}