




'''simple docstring'''
import math
def 							snake_case_    (  a__						:      int     ):



    """simple docstring"""




    if not isinstance(a__       ,a__     ):
        __lowercase     							=		f'Input value of [number={number}] must be an integer'
        raise TypeError(a__     )
    if number < 1:
        __lowercase     							=		f'Input value of [number={number}] must be a positive integer'
        raise ValueError(a__     )
    __lowercase     							=		[number]
    while number != 1:
        if number % 2 == 0:
            __lowercase     							=		math.floor(math.sqrt(a__     )     )
        else:
            __lowercase     							=		math.floor(
                math.sqrt(a__     ) * math.sqrt(a__     ) * math.sqrt(a__     )     )
        sequence.append(a__     )
    return sequence


if __name__ == "__main__":
  import doctest

  doctest.testmod()










'''simple docstring'''
from math import gcd
def 							snake_case_    (  a__						:      int = 1_20_00     ):



    """simple docstring"""




    __lowercase     							=		0
    for d in range(max_d + 1     ):
        for n in range(d // 3 + 1       ,(d + 1) // 2     ):
            if gcd(a__       ,a__     ) == 1:
                fractions_number += 1
    return fractions_number


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




