


def 						a__			(				A__				):

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


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









def 						a__			(				A__ = 5_0_0_0_0_0_0_0				):
			SCREAMING_SNAKE_CASE_		:     Union[str, Any]					=					set()
			SCREAMING_SNAKE_CASE_		:     Optional[int]					=					int((limit - 2_4) ** (1 / 2)				)

			SCREAMING_SNAKE_CASE_		:     Dict					=					set(range(3,      prime_square_limit + 1,      2				)				)
			primes.add(2				)
			for p in range(3,      prime_square_limit + 1,      2				):
						if p not in primes:
									continue
						primes.difference_update(set(range(p * p,      prime_square_limit + 1,      A__				)				)				)

			for primea in primes:
						SCREAMING_SNAKE_CASE_		:     int					=					primea * primea
						for primea in primes:
									SCREAMING_SNAKE_CASE_		:     Dict					=					primea * primea * primea
									if square + cube >= limit - 1_6:
												break
									for primea in primes:
												SCREAMING_SNAKE_CASE_		:     Optional[int]					=					primea * primea * primea * primea
												SCREAMING_SNAKE_CASE_		:     str					=					square + cube + tetr
												if total >= limit:
															break
												ret.add(A__				)

			return len(A__				)


if __name__ == "__main__":
				print(F"""{solution() = }""")





