



"""simple docstring"""







def       _lowerCamelCase				(							UpperCAmelCase_ :       int     )	-> list[int]:






	"""simple docstring"""





	if length <= 0 or not isinstance(UpperCAmelCase_,	UpperCAmelCase_     ):
		raise ValueError("Length must be a positive integer."     )
	return [n * (2 * n - 1) for n in range(UpperCAmelCase_     )]


if __name__ == "__main__":
			print(hexagonal_numbers(length=5))
			print(hexagonal_numbers(length=10))









"""simple docstring"""







def       _lowerCamelCase				(							UpperCAmelCase_ :       int     )	-> int:






	"""simple docstring"""





	if not isinstance(UpperCAmelCase_,	UpperCAmelCase_     ):
		raise ValueError("Input must be an integer"     )
	if input_num <= 0:
		raise ValueError("Input must be positive"     )
	return sum(
	    divisor for divisor in range(1,	input_num // 2 + 1     ) if input_num % divisor == 0     )


if __name__ == "__main__":
			import doctest

			doctest.testmod()




