mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 13:31:07 +00:00
56 lines
1.2 KiB
Python
56 lines
1.2 KiB
Python
from math import sqrt
|
|
|
|
"""
|
|
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.
|
|
"""
|
|
|
|
|
|
def sum_of_divisors(n):
|
|
total = 0
|
|
for i in range(1, int(sqrt(n) + 1)):
|
|
if n % i == 0 and i != sqrt(n):
|
|
total += i + n // i
|
|
elif i == sqrt(n):
|
|
total += i
|
|
return total - n
|
|
|
|
|
|
def solution(n):
|
|
"""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
|
|
for i in range(1, n)
|
|
if sum_of_divisors(sum_of_divisors(i)) == i and sum_of_divisors(i) != i
|
|
]
|
|
)
|
|
return total
|
|
|
|
|
|
if __name__ == "__main__":
|
|
print(solution(int(str(input()).strip())))
|