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33 lines
950 B
Python
33 lines
950 B
Python
"""Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.
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Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits:
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1634 = 1**4 + 6**4 + 3**4 + 4**4
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8208 = 8**4 + 2**4 + 0**4 + 8**4
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9474 = 9**4 + 4**4 + 7**4 + 4**4
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As 1 = 14 is not a sum it is not included.
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The sum of these numbers is 1634 + 8208 + 9474 = 19316.
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Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.
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"""
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def power_sums(n):
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numbers = []
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i = 9
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while i <= 10**(n+1):
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i = i + 1
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if int(max(str(i)))**n > i:
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continue
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s = sum([int(c)**n for c in str(i)])
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if i == s:
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numbers.append(i)
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return numbers
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def main():
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p = power_sums(4)
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print 'power_sums(4)', p, sum(p)
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p = power_sums(5)
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print 'power_sums(5)', p, sum(p)
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if __name__ == '__main__':
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main()
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