





from itertools import compress, repeat
from math import ceil, sqrt




def 			lowerCAmelCase_			(				UpperCamelCase_	)  ->		list[int]:

       if num <= 2:
              return []
       if num == 3:
              return [2]

       # Odd sieve for numbers in range [3, num - 1]
       UpperCamelCase_ 							=	bytearray(b"\x01"	) * ((num >> 1) - 1)

       for i in range(3       ,		int(sqrt(UpperCamelCase_	)	) + 1       ,		2	):
              if sieve[(i >> 1) - 1]:
                     UpperCamelCase_ 							=	i**2
                     UpperCamelCase_ 							=	repeat(
                         0       ,		ceil((num - i_squared) / (i << 1)	)	)

       return [2] + list(compress(range(3       ,		UpperCamelCase_       ,		2	)       ,		UpperCamelCase_	)	)


if __name__ == "__main__":
     import doctest

     doctest.testmod()





"""simple docstring"""
import math







def     _a					(   _SCREAMING_SNAKE_CASE					)     ->					list[int]:
							if not isinstance(_SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					):
														snake_case_     							=		f"""Input value of [number={number}] must be an integer"""
														raise TypeError(_SCREAMING_SNAKE_CASE					)
							if number < 1:
														snake_case_     							=		f"""Input value of [number={number}] must be a positive integer"""
														raise ValueError(_SCREAMING_SNAKE_CASE					)
							snake_case_     							=		[number]
							while number != 1:
														if number % 2 == 0:
																					snake_case_     							=		math.floor(math.sqrt(_SCREAMING_SNAKE_CASE					)					)
														else:
																					snake_case_     							=		math.floor(
																					    math.sqrt(_SCREAMING_SNAKE_CASE					) * math.sqrt(_SCREAMING_SNAKE_CASE					) * math.sqrt(_SCREAMING_SNAKE_CASE					)					)
														sequence.append(_SCREAMING_SNAKE_CASE					)
							return sequence


if __name__ == "__main__":
				import doctest

				doctest.testmod()



