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 PyPy3 (7.3.0) (judge verdict: Accepted)

#!/usr/bin/env python
n = int(input())
ans = 0 

is_primes = [True for _ in range(n+1)]
is_primes[0] = is_primes[1] = False
minFactor = [-1 for _ in range(n+1)]

for i in range(2, n+1):
    if not is_primes[i]: continue
    minFactor[i] = i 
    for j in range(i*i, n+1, i): 
        is_primes[j] = False
        minFactor[j] = i 


def fast_factorization(n):
    data = {}
    while n > 1:
        if minFactor[n] not in data:
            data[minFactor[n]] = 1 
        else:
            data[minFactor[n]] += 1
        n //= minFactor[n]
    return data


def count_divisors(n):
    ret = 1 
    for v in fast_factorization(n).values():
        ret *= (v+1)
    return ret 

for i in range(1, n): 
    ans += count_divisors(i)

print(ans)