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41 lines
1.3 KiB
Python
41 lines
1.3 KiB
Python
"""Evaluate the sum of all amicable pairs under 10000.
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Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).
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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.
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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.
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Evaluate the sum of all the amicable numbers under 10000.
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"""
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from e007 import is_prime
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from e012 import factor
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def proper_divisors(n):
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"""Returns the proper divisors of n
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Proper divisors are defined as numbers less than n which divide evenly into n
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"""
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divisors = factor(n)
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# Knock off the last factor, since it is equal to n
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return divisors[:-1]
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def main():
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MIN = 2
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MAX = 10000
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sums = {}
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amicable = []
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i = MIN
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while i < MAX:
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if not is_prime(i):
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s = sum(proper_divisors(i))
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sums[i] = s
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if s in sums and i == sums[s] and i != s:
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print i, s, sums[s]
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amicable.append(i)
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amicable.append(s)
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i = i + 1
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print 'Sum of amicable numbers less than {0}: {1}'.format(MAX, sum(amicable))
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if __name__ == '__main__':
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main()
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