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)

from collections import Counter

class Eratosthenes():  # エラトステネスの篩
    def __init__(self, N):  # 素数リスト生成 O(n*log(log n))
        self.fact = [i for i in range(N + 1)]
        for i in range(2, int(N ** 0.5) + 1):
            if self.fact[i] < i:
                continue
            for j in range(i ** 2, N + 1, i):
                self.fact[j] = i
        self.prime = [i for i in range(2, N + 1) if i == self.fact[i]]

    def factor(self, NUM):  # 高速素因数分解 O(log num)
        PRIME = []
        while NUM > 1:
            PRIME.append(self.fact[NUM])
            NUM //= self.fact[NUM]
        return Counter(PRIME)

n = int(input())

era = Eratosthenes(n)
ans = 0
for i in range(1, n):
    tmp = 1
    for num in era.factor(i).values():
        tmp *= num + 1
    ans += tmp
print(ans)