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: Accepted)

import math
N = int(input())

sqrt_N = math.floor(math.sqrt(N - 1))
conbination = 0
conbination_AeqB = 0
for A in range(1, sqrt_N + 1):

    # B = Aからfloor(N-1 / A)まで
    conbination_AeqB += 1
    conbination += math.floor((N - 1) / A) - A
    # N = 5
    # (1, 1, 4), (1, 2, 3), (1, 3, 2), (1, 4, 1)
    # (2, 1, 3), (2, 2, 1)
    # (3, 1, 2)
    # (4, 1, 1)
    # N = 4
    # (1, 1, 3), (1, 2, 2), (1, 3, 1)
    # (2, 1, 2)
    # (3, 1, 1)
print(conbination_AeqB + conbination * 2)