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 proconio::input;
//use itertools::Itertools;
use std::collections::HashMap;

fn prime_factor(n: i128) -> HashMap<i128,i128> {
    let mut n = n;
    let mut ret = HashMap::new();
    let mut i = 2;
    while i * i <= n {
        let mut tmp : i128 = 0;
        while n % i == 0 {
            tmp += 1;
            n /= i;
        }
        ret.insert(i, tmp);
        i += 1;
    }
    if n != 1 { ret.insert(n, 1); }
    ret
}

fn divisor_num(n : i128) -> i128 {
    let pf : HashMap<i128, i128> = prime_factor(n);
    let mut ret : i128 = pf.iter()
        .map(|(_, v)| v+1).product();
    ret
}

fn main() {
    input!{n : i128};
    let mut total : i128 = 0;
    for c in 1..n {
        total += divisor_num(n - c);
    }
    println!("{}", total);
}