#### Hamming Numbers

p
```"""
A Hamming number is a positive integer of the form 2^i*3^j*5^k, for some
non-negative integers i, j, and k. They are often referred to as regular numbers.
"""

def hamming(n_element: int) -> list:
"""
This function creates an ordered list of n length as requested, and afterwards
returns the last value of the list. It must be given a positive integer.

:param n_element: The number of elements on the list
:return: The nth element of the list

>>> hamming(5)
[1, 2, 3, 4, 5]
>>> hamming(10)
[1, 2, 3, 4, 5, 6, 8, 9, 10, 12]
>>> hamming(15)
[1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24]
"""
n_element = int(n_element)
if n_element < 1:
my_error = ValueError("a should be a positive number")
raise my_error

hamming_list = 
i, j, k = (0, 0, 0)
index = 1
while index < n_element:
while hamming_list[i] * 2 <= hamming_list[-1]:
i += 1
while hamming_list[j] * 3 <= hamming_list[-1]:
j += 1
while hamming_list[k] * 5 <= hamming_list[-1]:
k += 1
hamming_list.append(
min(hamming_list[i] * 2, hamming_list[j] * 3, hamming_list[k] * 5)
)
index += 1
return hamming_list

if __name__ == "__main__":
n = input("Enter the last number (nth term) of the Hamming Number Series: ")
print("Formula of Hamming Number Series => 2^i * 3^j * 5^k")
hamming_numbers = hamming(int(n))
print("-----------------------------------------------------")
print(f"The list with nth numbers is: {hamming_numbers}")
print("-----------------------------------------------------")
```  