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021.py
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021.py
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#/bin/python
# 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 prime
def is_amical(n):
sum1 = sum(prime.get_divisors(n)-set([n]))
sum2 = sum(prime.get_divisors(sum1)-set([sum1]))
#print( n, sum1, sum2 )
return n == sum2 and n != sum1
#print( is_amical(219) )
#print( is_amical(220) )
#print( is_amical(221) )
mylist = [n for n in range(2,10000) if is_amical(n)]
#print( mylist )
mysum = sum(mylist)
print( mysum ) # 31626