Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits:

1634 = 1⁴ + 6⁴ + 3⁴ + 4⁴
8208 = 8⁴ + 2⁴ + 0⁴ + 8⁴
9474 = 9⁴ + 4⁴ + 7⁴ + 4⁴

As 1 = 1⁴ is not a sum it is not included.

The sum of these numbers is 1634 + 8208 + 9474 = 19316.

Find the sum of all the numbers that can be written as the sum of fifth powers of their digits



In [1]:

    
pow5 = dict(((str(i), i ** 5) for i in range(10)))
pow5









    Out[1]:





{'0': 0,
 '1': 1,
 '2': 32,
 '3': 243,
 '4': 1024,
 '5': 3125,
 '6': 7776,
 '7': 16807,
 '8': 32768,
 '9': 59049}



In [2]:

    
def foo():
    j = []
    for i in range(2, 1000000):
        if i == sum((pow5[c] for c in str(i))):
            j.append(i)
    return sum(j)



In [3]:

    
%timeit foo()
foo()









    



1 loops, best of 3: 2.46 s per loop






    Out[3]:





443839