





from math import isqrt, loga

def     snake_case							(UpperCamelCase			:     List[str]							):




	'''simple docstring'''







	lowerCamelCase__										=			[True] * max_number
	for i in range(2			,    isqrt(max_number - 1							) + 1							):
		if is_prime[i]:
			for j in range(i**2			,    UpperCamelCase			,    UpperCamelCase							):
				lowerCamelCase__										=			False

	return [i for i in range(2			,    UpperCamelCase							) if is_prime[i]]

def     snake_case							(UpperCamelCase			:     Optional[int] = 800800			,    UpperCamelCase			:     List[str] = 800800							):




	'''simple docstring'''







	lowerCamelCase__										=			degree * loga(UpperCamelCase							)
	lowerCamelCase__										=			int(UpperCamelCase							)
	lowerCamelCase__										=			calculate_prime_numbers(UpperCamelCase							)

	lowerCamelCase__										=			0
	lowerCamelCase__										=			0
	lowerCamelCase__										=			len(UpperCamelCase							) - 1
	while left < right:
		while (
		    prime_numbers[right] * loga(prime_numbers[left]							)
		    + prime_numbers[left] * loga(prime_numbers[right]							)
		    > upper_bound
		):
			right -= 1
		hybrid_integers_count += right - left
		left += 1

	return hybrid_integers_count


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






'''simple docstring'''


def 						lowerCamelCase__   (				a							):
						__snake_case						 =   int(a							)
						if n_element < 1:
												__snake_case						 =   ValueError('a should be a positive number'							)
												raise my_error

						__snake_case						 =   [1]
						__snake_case ,       __snake_case ,       __snake_case						 =   (0, 0, 0)
						__snake_case						 =   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__":
	_lowercase  =			input("""Enter the last number (nth term) of the Hamming Number Series: """)
	print("""Formula of Hamming Number Series => 2^i * 3^j * 5^k""")
	_lowercase  =			hamming(int(n))
	print("""-----------------------------------------------------""")
	print(f'''The list with nth numbers is: {hamming_numbers}''')
	print("""-----------------------------------------------------""")

