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prob21.py
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prob21.py
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# coding=utf-8
"""
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 amicable(n):
d1 = sum(utils.divisors(n))
if sum(utils.divisors(d1)) == n:
if d1 != n:
return d1
else:
return 0
else:
return 0
def main(n):
pairs = []
for a in xrange(n):
b = amicable(a)
if bool(b) and a < n and b < n:
# print a, b
if utils.list_has(pairs, a) or utils.list_has(pairs, b):
None
else:
pairs.append(a)
pairs.append(b)
print sum(pairs)
if __name__ == '__main__':
main(10000)