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)

import sys
import math

if __name__ == '__main__':
    N = int(sys.stdin.readline().rstrip())
    # N = 1000000
    # N = 100
    ans = 0

    for i in range(1, N+1):
        AB = N-i
        tmp = 0
        # for j in range(1, math.ceil(math.log2(AB+1)+1)):
        # for j in range(1, int(math.sqrt(AB+1)+1)):
        # for j in range(1, int(math.sqrt(AB+1))):
        for j in range(1, AB+1):
            if AB % j == 0:
                if AB / j <= j:
                    tmp *= 2
                    if AB / j == j:
                        tmp += 1
                    break
                else:
                    tmp += 1
        ans += tmp
    print(ans)

# 3*33
# 1,99 3,33 9,11 11,9 33,3 99,1