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solve21.py
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solve21.py
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# https://projecteuler.net/problem=21
# Run with: 'python solve21.py'
# using Python 3.6.9
# by Zack Sargent
# Prompt:
# 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 10_000.
# this is d(n) from the prompt.
def get_sum_of_divisors(num: int) -> int:
if num < 2:
return num
total = 0
i = 1
while i ** 2 < num:
if num % i == 0:
if num / i == i:
total += i
else:
total += i
total += num//i
i += 1
total -= num
return total
def has_amicable(a: int) -> bool:
if a < 2:
raise Exception("Invalid domain")
b = get_sum_of_divisors(a)
a_inverse = get_sum_of_divisors(b)
return (a == a_inverse and a != b)
total = 0
for a in range(2, 10_000):
if has_amicable(a):
total += a
print(total)
# -> 31626