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)

#![allow(unused_imports)]
#![allow(unused_macros)]
use itertools::Itertools;
use std::cmp::{max, min};
use std::collections::*;
use std::i64;
use std::io::{stdin, Read};
use std::usize;

trait ChMinMax {
    fn chmin(&mut self, other: Self);
    fn chmax(&mut self, other: Self);
}
impl<T> ChMinMax for T
where
    T: PartialOrd,
{
    fn chmin(&mut self, other: Self) {
        if *self > other {
            *self = other
        }
    }
    fn chmax(&mut self, other: Self) {
        if *self < other {
            *self = other
        }
    }
}

#[allow(unused_macros)]
macro_rules! parse {
    ($it: ident ) => {};
    ($it: ident, ) => {};
    ($it: ident, $var:ident : $t:tt $($r:tt)*) => {
        let $var = parse_val!($it, $t);
        parse!($it $($r)*);
    };
    ($it: ident, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = parse_val!($it, $t);
        parse!($it $($r)*);
    };
    ($it: ident, $var:ident $($r:tt)*) => {
        let $var = parse_val!($it, usize);
        parse!($it $($r)*);
    };
}

#[allow(unused_macros)]
macro_rules! parse_val {
    ($it: ident, [$t:tt; $len:expr]) => {
        (0..$len).map(|_| parse_val!($it, $t)).collect::<Vec<_>>();
    };
    ($it: ident, ($($t: tt),*)) => {
        ($(parse_val!($it, $t)),*)
    };
    ($it: ident, u1) => {
        $it.next().unwrap().parse::<usize>().unwrap() -1
    };
    ($it: ident, $t: ty) => {
        $it.next().unwrap().parse::<$t>().unwrap()
    };
}

pub fn factor(mut n: usize) -> HashMap<usize, usize> {
    let mut ret = std::collections::HashMap::new();
    let n0 = n;
    let mut cur = 2;
    while cur * cur <= n0 {
        if n % cur != 0 {
            cur += 1;
            continue;
        }
        let mut count = 0;
        while n % cur == 0 {
            n /= cur;
            count += 1;
        }
        ret.insert(cur, count);
        cur += 1;
    }
    if n > 1 {
        ret.insert(n, 1);
    }
    ret
}

pub fn num_divs(mut n: usize, memo: &mut HashMap<usize, usize>) -> usize {
    if let Some(ret) = memo.get(&n) {
        return *ret;
    }
    let n0 = n;
    let mut cur = 2;
    let mut ret = 1;
    while cur * cur <= n0 {
        if n % cur != 0 {
            cur += 1;
            continue;
        }
        let mut count = 0;
        while n % cur == 0 {
            n /= cur;
            count += 1;
        }
        ret *= count + 1;
        cur += 1;
    }
    if n > 1 {
        ret *= 2;
    }
    memo.insert(n0, ret);
    ret
}
fn solve(s: &str) {
    let mut it = s.split_whitespace();
    parse!(it, n: usize);
    let mut count = 0;
    let mut memo = HashMap::new();
    for c in 1..n {
        let ab = n - c;
        count += num_divs(ab, &mut memo);
    }
    println!("{}", count);
}

fn main() {
    let mut s = String::new();
    stdin().read_to_string(&mut s).unwrap();
    solve(&s);
}

#[cfg(test)]
mod tests {
    use super::*;
    #[test]
    fn test_input() {
        let s = "
        ";
        solve(s);
    }
}