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 numba import njit

@njit
def factorize1(n):
    ans=dict()
    i = 2
    while i*i<=n:
        while n%i==0:
            n=n//i
            if i in ans:
                ans[i]+=1
            else:
                ans[i]=1
        i+=1
    if n!=1:
        ans[n]=1
        
    div=1
    for j in ans.items():
        div *= j[1]+1
    return div
   
N=int(input())
ans=1
for k in range(2,N):
    ans += factorize1(k)
print(ans)