




from __future__ import annotations





def 	__A	(			__lowerCamelCase							,    __lowerCamelCase							,    __lowerCamelCase							,    )   -> list[float | int]:
	if not all((nth_term, start_term_a, common_ratio_r)					):
		return []
	a		       =							[]
	a		       =							1
	a		       =							common_ratio_r
	for _ in range(int(__lowerCamelCase					)					):
		if not series:
			series.append(__lowerCamelCase					)
		else:
			power += 1
			series.append(float(start_term_a * multiple					)					)
			a		       =							pow(float(__lowerCamelCase					)							,    __lowerCamelCase					)
	return series


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		__UpperCamelCase      : Dict					      =   float(input("Enter the last number (n term) of the Geometric Series"))
		__UpperCamelCase      : int					      =   float(input("Enter the starting term (a) of the Geometric Series"))
		__UpperCamelCase      : Any					      =   float(
		    input("Enter the common ratio between two terms (r) of the Geometric Series")
		)
		print("Formula of Geometric Series => a + ar + ar^2 ... +ar^n")
		print(geometric_series(nth_term, start_term_a, common_ratio_r))







import math





def 	__A	(			__lowerCamelCase					)   -> bool:

	if 1 < number < 4:
		# 2 and 3 are primes
		return True
	elif number < 2 or number % 2 == 0 or number % 3 == 0:
		# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
		return False

	# All primes number are in format of 6k +/- 1
	for i in range(5							,    int(math.sqrt(__lowerCamelCase					) + 1					)							,    6					):
		if number % i == 0 or number % (i + 2) == 0:
			return False
	return True





def 	__A	(			__lowerCamelCase = 6008_5147_5143					)   -> int:

	try:
		a		       =							int(__lowerCamelCase					)
	except (TypeError, ValueError):
		raise TypeError("""Parameter n must be int or castable to int."""					)
	if n <= 0:
		raise ValueError("""Parameter n must be greater than or equal to one."""					)
	a		       =							0
	if is_prime(__lowerCamelCase					):
		return n
	while n % 2 == 0:
		n //= 2
	if is_prime(__lowerCamelCase					):
		return n
	for i in range(3							,    int(math.sqrt(__lowerCamelCase					)					) + 1							,    2					):
		if n % i == 0:
			if is_prime(n // i					):
				a		       =							n // i
				break
			elif is_prime(__lowerCamelCase					):
				a		       =							i
	return max_number


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

