






'''simple docstring'''



from math import isqrt, loga



def    __UpperCAmelCase	(				SCREAMING_SNAKE_CASE__:	int    )  ->			list[int]:

   """simple docstring"""
   __a				     =    [True] * max_number
   for i in range(2,					isqrt(max_number - 1    ) + 1    ):
      if is_prime[i]:
         for j in range(i**2,					SCREAMING_SNAKE_CASE__,					SCREAMING_SNAKE_CASE__    ):
            __a				     =    False

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



def    __UpperCAmelCase	(				SCREAMING_SNAKE_CASE__:	int = 800800,					SCREAMING_SNAKE_CASE__:	int = 800800    )  ->			int:

   """simple docstring"""
   __a				     =    degree * loga(SCREAMING_SNAKE_CASE__    )
   __a				     =    int(SCREAMING_SNAKE_CASE__    )
   __a				     =    calculate_prime_numbers(SCREAMING_SNAKE_CASE__    )

   __a				     =    0
   __a				     =    0
   __a				     =    len(SCREAMING_SNAKE_CASE__    ) - 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'''



from maths.prime_factors import prime_factors



def    __UpperCAmelCase	(				SCREAMING_SNAKE_CASE__:	int    )  ->			int:

   """simple docstring"""
   if not isinstance(SCREAMING_SNAKE_CASE__,					SCREAMING_SNAKE_CASE__    ):
      __a				     =    f"""Input value of [number={number}] must be an integer"""
      raise TypeError(SCREAMING_SNAKE_CASE__    )
   if number < 1:
      raise ValueError('Input must be a positive integer'    )
   return -1 if len(prime_factors(SCREAMING_SNAKE_CASE__    )    ) % 2 else 1


if __name__ == "__main__":
 import doctest

 doctest.testmod()