Buggy python submission (verdict: Time Limit Exceeded):
import collections
import math

N_ = 10 ** 3
A=list(range(2,N_+1))
p=list()
while A[0]**2<=N_:
	tmp=A[0]
	p.append(tmp)
	A=[e for e in A if e%tmp!=0]
p_list = p+A

def search_divisor_num_1(num):
    if num < 0:
        return None
    elif num == 1:
        return 1
    else:
        num_sqrt = math.floor(math.sqrt(num))

        divisor_num = 1
        for prime in p_list:
            count = 1
            while num % prime == 0:
                num //= prime
                count += 1
            divisor_num *= count

        if num != 1:
            divisor_num *= 2

        return divisor_num
    
def main():
    N = int(input())
    ans = 0
    for c in range(1, N):
        ans += search_divisor_num_1(N - c)
    return ans
 
if __name__ == '__main__':
    print(main())

Fixed submission:
def get_sieve_of_eratosthenes(n):
    if not isinstance(n, int):
        raise TypeError("n is int-type.")
    if n < 2:
        raise ValueError("n is more than 2")
    data = [i for i in range(2, n + 1)]
    for d in data:
        data = [x for x in data if (x == d or x % d != 0)]
    return data
 
p_list = get_sieve_of_eratosthenes(10**3)
 
def factorization_counta(n):
    arr = []
    temp = n
    for i in p_list:
        if i * i > n:
            break
        elif temp % i == 0:
            cnt = 0
            while temp % i == 0:
                cnt += 1
                temp //= i
            arr.append(cnt)
            
    if temp != 1:
        arr.append(1)
    if arr == []:
        arr.append(1)
    return arr

def main():
    N = int(input())
    ans = 1
    for c in range(2, N):
        p = factorization_counta(c)
        tmp = 1
        for v in p:
            tmp *= (v + 1)
        ans += tmp
    return ans
 
if __name__ == '__main__':
    print(main())

Buggy python submission (verdict: Time Limit Exceeded):
def get_sieve_of_eratosthenes(n):
    if not isinstance(n, int):
        raise TypeError("n is int-type.")
    if n < 2:
        raise ValueError("n is more than 2")
    data = [i for i in range(2, n + 1)]
    for d in data:
        data = [x for x in data if (x == d or x % d != 0)]
    return data
 
p_list = get_sieve_of_eratosthenes(10**3)
 
# def factorization_counta(n):
#     arr = []
#     temp = n
#     for i in p_list:
#         if i * i > n:
#             break
#         elif temp % i == 0:
#             cnt = 0
#             while temp % i == 0:
#                 cnt += 1
#                 temp //= i
#             arr.append(cnt)
            
#     if temp != 1:
#         arr.append(1)
#     if arr == []:
#         arr.append(1)
#     return arr

def prime(m):
    pf = {}
    for i in p_list:
        while m%i==0:
            pf[i]=pf.get(i,0)+1
            m//=i
    if m>1:pf[m]=1
    return pf
 
def main():
    N = int(input())
    ans = 0
    for c in range(1, N):
        p = prime(N - c)
        tmp = 1
        for v in p.values():
            tmp *= (v + 1)
        ans += tmp
    return ans
 
if __name__ == '__main__':
    print(main())

Fixed submission:
def get_sieve_of_eratosthenes(n):
    if not isinstance(n, int):
        raise TypeError("n is int-type.")
    if n < 2:
        raise ValueError("n is more than 2")
    data = [i for i in range(2, n + 1)]
    for d in data:
        data = [x for x in data if (x == d or x % d != 0)]
    return data
 
p_list = get_sieve_of_eratosthenes(10**3)
 
def factorization_counta(n):
    arr = []
    temp = n
    for i in p_list:
        if i * i > n:
            break
        elif temp % i == 0:
            cnt = 0
            while temp % i == 0:
                cnt += 1
                temp //= i
            arr.append(cnt)
            
    if temp != 1:
        arr.append(1)
    if arr == []:
        arr.append(1)
    return arr

def main():
    N = int(input())
    ans = 1
    for c in range(2, N):
        p = factorization_counta(c)
        tmp = 1
        for v in p:
            tmp *= (v + 1)
        ans += tmp
    return ans
 
if __name__ == '__main__':
    print(main())

Buggy python submission (verdict: Time Limit Exceeded):
import math

def prime(m):
    pf = {}
    for i in range(2,int(m**0.5)+1):
        while m%i==0:
            pf[i]=pf.get(i,0)+1
            m//=i
    if m>1:pf[m]=1
    return pf

def calc_tmpans(primes, tmpans, cnt, val):
    if len(primes) == 0:
        tmpans[val] = cnt
    else:
        (p, v) = primes[0]
        for i in range(v + 1):
            calc_tmpans(primes[1:], tmpans, cnt * (i + 1), val * (p ** i) )

def main():
    N = int(input())

    tmpans = [0]*(N+1)
    ans = 0
    for c in reversed(range(1, N)):
        if tmpans[N - c] != 0:
            ans += tmpans[N-c]
        else:
            p = prime(N - c)
            tmp = 1
            p_list = list(p.items())
            # for (k, v) in p_list:
            #     tmp *= (v + 1)
            calc_tmpans(p_list, tmpans, 1, 1)
            ans += tmp
    return sum(tmpans)

if __name__ == '__main__':
    print(main())

Fixed submission:
def get_sieve_of_eratosthenes(n):
    if not isinstance(n, int):
        raise TypeError("n is int-type.")
    if n < 2:
        raise ValueError("n is more than 2")
    data = [i for i in range(2, n + 1)]
    for d in data:
        data = [x for x in data if (x == d or x % d != 0)]
    return data
 
p_list = get_sieve_of_eratosthenes(10**3)
 
def factorization_counta(n):
    arr = []
    temp = n
    for i in p_list:
        if i * i > n:
            break
        elif temp % i == 0:
            cnt = 0
            while temp % i == 0:
                cnt += 1
                temp //= i
            arr.append(cnt)
            
    if temp != 1:
        arr.append(1)
    if arr == []:
        arr.append(1)
    return arr

def main():
    N = int(input())
    ans = 1
    for c in range(2, N):
        p = factorization_counta(c)
        tmp = 1
        for v in p:
            tmp *= (v + 1)
        ans += tmp
    return ans
 
if __name__ == '__main__':
    print(main())

Buggy python submission (verdict: Time Limit Exceeded):
import math

def prime(m):
    pf = {}
    for i in range(2,int(m**0.5)+1):
        while m%i==0:
            pf[i]=pf.get(i,0)+1
            m//=i
    if m>1:pf[m]=1
    return pf

def calc_tmpans(primes, tmpans, cnt, val):
    if len(primes) == 0:
        tmpans[val] = cnt
    else:
        (p, v) = primes[0]
        for i in range(v + 1):
            calc_tmpans(primes[1:], tmpans, cnt * (i + 1), val * (p ** i) )

def main():
    N = int(input())

    tmpans = [0]*(N+1)
    ans = 0
    for c in range(1, N):
        if tmpans[N - c] != 0:
            ans += tmpans[N-c]
        else:
            p = prime(N - c)
            tmp = 1
            p_list = list(p.items())
            # for (k, v) in p_list:
            #     tmp *= (v + 1)
            calc_tmpans(p_list, tmpans, 1, 1)
            ans += tmp
    return sum(tmpans)

if __name__ == '__main__':
    print(main())

Fixed submission:
def get_sieve_of_eratosthenes(n):
    if not isinstance(n, int):
        raise TypeError("n is int-type.")
    if n < 2:
        raise ValueError("n is more than 2")
    data = [i for i in range(2, n + 1)]
    for d in data:
        data = [x for x in data if (x == d or x % d != 0)]
    return data
 
p_list = get_sieve_of_eratosthenes(10**3)
 
def factorization_counta(n):
    arr = []
    temp = n
    for i in p_list:
        if i * i > n:
            break
        elif temp % i == 0:
            cnt = 0
            while temp % i == 0:
                cnt += 1
                temp //= i
            arr.append(cnt)
            
    if temp != 1:
        arr.append(1)
    if arr == []:
        arr.append(1)
    return arr

def main():
    N = int(input())
    ans = 1
    for c in range(2, N):
        p = factorization_counta(c)
        tmp = 1
        for v in p:
            tmp *= (v + 1)
        ans += tmp
    return ans
 
if __name__ == '__main__':
    print(main())

Buggy python submission (verdict: Time Limit Exceeded):
import math

def prime(m):
    pf = {}
    for i in range(2,int(m**0.5)+1):
        while m%i==0:
            pf[i]=pf.get(i,0)+1
            m//=i
    if m>1:pf[m]=1
    return pf

def main():
    N = int(input())
    ans = 0
    for c in range(1, N):
        p = prime(N - c)
        tmp = 1
        for v in p.values():
            tmp *= (v + 1)
        ans += tmp
    return ans

if __name__ == '__main__':
    print(main())

Fixed submission:
def get_sieve_of_eratosthenes(n):
    if not isinstance(n, int):
        raise TypeError("n is int-type.")
    if n < 2:
        raise ValueError("n is more than 2")
    data = [i for i in range(2, n + 1)]
    for d in data:
        data = [x for x in data if (x == d or x % d != 0)]
    return data
 
p_list = get_sieve_of_eratosthenes(10**3)
 
def factorization_counta(n):
    arr = []
    temp = n
    for i in p_list:
        if i * i > n:
            break
        elif temp % i == 0:
            cnt = 0
            while temp % i == 0:
                cnt += 1
                temp //= i
            arr.append(cnt)
            
    if temp != 1:
        arr.append(1)
    if arr == []:
        arr.append(1)
    return arr

def main():
    N = int(input())
    ans = 1
    for c in range(2, N):
        p = factorization_counta(c)
        tmp = 1
        for v in p:
            tmp *= (v + 1)
        ans += tmp
    return ans
 
if __name__ == '__main__':
    print(main())

Buggy python submission (verdict: Time Limit Exceeded):
import math
def main():
    N = int(input())
    ans = 0
    for c in range(1, N):
        tmp = 0
        sqrtnc = int(math.sqrt(N - c))
        for b in range(1, sqrtnc + 1):
            if ((N - c) // b) * b == N - c:
                tmp += 1
        ans += tmp * 2
        if sqrtnc ** 2 == N - c:
            ans -= 1
    return ans

if __name__ == '__main__':
    print(main())

Fixed submission:
def get_sieve_of_eratosthenes(n):
    if not isinstance(n, int):
        raise TypeError("n is int-type.")
    if n < 2:
        raise ValueError("n is more than 2")
    data = [i for i in range(2, n + 1)]
    for d in data:
        data = [x for x in data if (x == d or x % d != 0)]
    return data
 
p_list = get_sieve_of_eratosthenes(10**3)
 
def factorization_counta(n):
    arr = []
    temp = n
    for i in p_list:
        if i * i > n:
            break
        elif temp % i == 0:
            cnt = 0
            while temp % i == 0:
                cnt += 1
                temp //= i
            arr.append(cnt)
            
    if temp != 1:
        arr.append(1)
    if arr == []:
        arr.append(1)
    return arr

def main():
    N = int(input())
    ans = 1
    for c in range(2, N):
        p = factorization_counta(c)
        tmp = 1
        for v in p:
            tmp *= (v + 1)
        ans += tmp
    return ans
 
if __name__ == '__main__':
    print(main())

Buggy python submission (verdict: Time Limit Exceeded):
def make_divisors(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)
    return divisors

def main():
    N = int(input())
    ans = 0
    for c in range(1, N):
        ans += len(make_divisors(N - c))
    return ans

if __name__ == '__main__':
    print(main())

Fixed submission:
def get_sieve_of_eratosthenes(n):
    if not isinstance(n, int):
        raise TypeError("n is int-type.")
    if n < 2:
        raise ValueError("n is more than 2")
    data = [i for i in range(2, n + 1)]
    for d in data:
        data = [x for x in data if (x == d or x % d != 0)]
    return data
 
p_list = get_sieve_of_eratosthenes(10**3)
 
def factorization_counta(n):
    arr = []
    temp = n
    for i in p_list:
        if i * i > n:
            break
        elif temp % i == 0:
            cnt = 0
            while temp % i == 0:
                cnt += 1
                temp //= i
            arr.append(cnt)
            
    if temp != 1:
        arr.append(1)
    if arr == []:
        arr.append(1)
    return arr

def main():
    N = int(input())
    ans = 1
    for c in range(2, N):
        p = factorization_counta(c)
        tmp = 1
        for v in p:
            tmp *= (v + 1)
        ans += tmp
    return ans
 
if __name__ == '__main__':
    print(main())