Поиск количества делителей числа n

divisors = {}
 
 
def number_of_divisors(n):
    if n not in divisors.keys():
        c = 1
        for i in range(1, int(n // 2) + 1):
            if n % i == 0:
                c += 1
        divisors[n] = c
        return c
    else:
        return divisors[n]
 
 
print(number_of_divisors(2000000000))
print(number_of_divisors(6))
print(number_of_divisors(6))
print(number_of_divisors(2000000000))
print(divisors)

def number_of_divisors(n, d=2, ord=1):
    num = n
    if n not in divisors.keys():
        while d*d <= n:
            tmp = 1
            while n%d == 0:
                tmp += 1
                n //= d
            else:
                ord *= tmp
            d += 1
        ord *= (n>1) + 1
        divisors[num] = ord
        return ord
    else:
        return divisors[num]

divisors = {}
 
 
def number_of_divisors(n):
    count = 0
    if n not in divisors:
        for i in range(1, int(n ** 0.5) + 1):
            count += n % i == 0
        divisors[n] = count * 2
        if n == int(n ** 0.5) ** 2:
            divisors[n] -= 1
    return divisors[n]
 
 
 
print(number_of_divisors(2000000000))
print(number_of_divisors(6))
print(number_of_divisors(6))
print(number_of_divisors(2000000000))
print(divisors)
 
print(number_of_divisors(25))
print(number_of_divisors(121))
print(number_of_divisors(144))
print(number_of_divisors(625))
print(divisors)