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 Python (3.8.2) (judge verdict: Time Limit Exceeded)

from operator import mul
from functools import reduce

def main():
    def factorization(n):
        l = []
        tmp = n
        for i in range(2, int(-(-tmp**0.5//1))+1):
            if tmp%i == 0:
                cnt = 0
                while tmp%i == 0:
                    cnt += 1
                    tmp //= i
                l.append(cnt+1)
                i += 1
        if tmp != 1:
            l.append(2)
        if l == []:
            if n != 1:
                l.append(2)
        if n == 1:
            l = [2]
        return l

    n = int(input())
    cnt = 0
    i = n
    for i in range(1, n):
        div = factorization(n-i)
        pattern = reduce(mul, div)
        cnt += pattern
    print(cnt-1) 
    
if __name__ == '__main__':
    main()