sol1.py

"""
Amicable Numbers
Problem 21

Let d(n) be defined as the sum of proper divisors of n (numbers less than n
which divide evenly into n).
If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and
each of a and b are called amicable numbers.

For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55
and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and
142; so d(284) = 220.

Evaluate the sum of all the amicable numbers under 10000.
"""

frommathimportsqrt


defsum_of_divisors(n: int) ->int:
total=0
foriinrange(1, int(sqrt(n) +1)):
ifn%i==0andi!=sqrt(n):
total+=i+n//i
elifi==sqrt(n):
total+=i
returntotal-n


defsolution(n: int=10000) ->int:
"""Returns the sum of all the amicable numbers under n.

 >>> solution(10000)
 31626
 >>> solution(5000)
 8442
 >>> solution(1000)
 504
 >>> solution(100)
 0
 >>> solution(50)
 0
 """
total=sum(
i
foriinrange(1, n)
ifsum_of_divisors(sum_of_divisors(i)) ==iandsum_of_divisors(i) !=i
 )
returntotal


if__name__=="__main__":
print(solution(int(str(input()).strip())))