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: Time Limit Exceeded)

import math as mt

MAXN = 1000001

spf = [0 for i in range(MAXN)]



def sieve():
    spf[1] = 1
    for i in range(2, MAXN):

        
        spf[i] = i

    for i in range(4, MAXN, 2):
        spf[i] = 2

    for i in range(3, mt.ceil(mt.sqrt(MAXN))):

        if (spf[i] == i):

            for j in range(i * i, MAXN, i):

                if (spf[j] == j):
                    spf[j] = i



def getFactorization(x):
    ret = [0]*(x+1)
    while (x != 1):
        ret[spf[x]]+=1
        x = x // spf[x]

    return ret

sieve()
x = int(input())
ans = 0
for i in range(1,x):
    p = getFactorization(x-i)
    sumi=1
    for i in range(len(p)):
        sumi*=(1+p[i])
    ans+=sumi
print(ans)