






"""simple docstring"""




def 			lowerCAmelCase__     (     UpperCamelCase__=2_8_1_2_3				):



  '''simple docstring'''
  _a  :       int             =	[1] * (limit + 1)

  for i in range(2     ,   int(limit**0.5				) + 1				):
    sum_divs[i * i] += i
    for k in range(i + 1     ,   limit // i + 1				):
      sum_divs[k * i] += k + i

  _a  :       Optional[int]             =	set()
  _a  :       Union[str, Any]             =	0

  for n in range(1     ,   limit + 1				):
    if sum_divs[n] > n:
      abundants.add(UpperCamelCase__				)

    if not any((n - a in abundants) for a in abundants				):
      res += n

  return res


if __name__ == "__main__":
 print(solution())









"""simple docstring"""




def 			lowerCAmelCase__     (     UpperCamelCase__     ,   UpperCamelCase__     ,   UpperCamelCase__     ,   UpperCamelCase__     ,   UpperCamelCase__     ,   ):



  '''simple docstring'''
  _a  :       Optional[Any]             =	[redshift, radiation_density, matter_density, dark_energy]
  if any(p < 0 for p in parameters				):
    raise ValueError("""All input parameters must be positive"""				)

  if any(p > 1 for p in parameters[1:4]				):
    raise ValueError("""Relative densities cannot be greater than one"""				)
  else:
    _a  :       Tuple             =	1 - (matter_density + radiation_density + dark_energy)

    _a  :       int             =	(
        radiation_density * (redshift + 1) ** 4
        + matter_density * (redshift + 1) ** 3
        + curvature * (redshift + 1) ** 2
        + dark_energy
    )

    _a  :       List[str]             =	hubble_constant * e_a ** (1 / 2)
    return hubble


if __name__ == "__main__":
 import doctest

 # run doctest
 doctest.testmod()

 # demo LCDM approximation
 _snake_case          =   0.3

 print(
     hubble_parameter(
         hubble_constant=68.3,
         radiation_density=1e-4,
         matter_density=matter_density,
         dark_energy=1 - matter_density,
         redshift=0,
     )
 )

