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21_amicable_numbers.py
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21_amicable_numbers.py
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# http://projecteuler.net/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.
import utils
def are_amicable(a, b):
"""
>>> are_amicable(220, 284)
True
"""
if a == b:
return False
return (utils.sum_of_proper_divisors(a) == b and utils.sum_of_proper_divisors(b) == a)
def main():
l = set()
amicable_total = 0
for a in xrange(1, 10001):
if not a % 500:
print a
# doing this calc twice, could cache or pass in
b = utils.sum_of_proper_divisors(a)
if are_amicable(a, b):
l.add(a)
l.add(b)
print l
return sum(l)
if __name__ == "__main__":
import doctest
doctest.testmod()
print main()