






def 						a    (		lowerCamelCase_       ):






				'''simple docstring'''
				if not isinstance(lowerCamelCase_	,     lowerCamelCase_       ):
								raise ValueError('''Input must be an integer'''       )
				if input_num <= 0:
								raise ValueError('''Input must be positive'''       )
				return sum(
				    divisor for divisor in range(1	,     input_num // 2 + 1       ) if input_num % divisor == 0       )


if __name__ == "__main__":
							import doctest

							doctest.testmod()












from collections import defaultdict
from math import gcd






def 						a    (		lowerCamelCase_ = 150_0000       ):






				'''simple docstring'''
				lowercase__     				=    defaultdict(lowerCamelCase_       )
				lowercase__     				=    2
				while 2 * euclid_m * (euclid_m + 1) <= limit:
								for euclid_n in range((euclid_m % 2) + 1	,     lowerCamelCase_	,     2       ):
												if gcd(lowerCamelCase_	,     lowerCamelCase_       ) > 1:
																continue
												lowercase__     				=    2 * euclid_m * (euclid_m + euclid_n)
												for perimeter in range(lowerCamelCase_	,     limit + 1	,     lowerCamelCase_       ):
																frequencies[perimeter] += 1
								euclid_m += 1
				return sum(1 for frequency in frequencies.values() if frequency == 1       )


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




