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"""

Problem 119: https://projecteuler.net/problem=119

Name: Digit power sum

The number 512 is interesting because it is equal to the sum of its digits

raised to some power: 5 + 1 + 2 = 8, and 8^3 = 512. Another example of a number

with this property is 614656 = 28^4. We shall define an to be the nth term of

this sequence and insist that a number must contain at least two digits to have a sum.

You are given that a2 = 512 and a10 = 614656. Find a30

"""

import math

def digit_sum(n: int) -> int:

"""

Returns the sum of the digits of the number.

>>> digit_sum(123)

>>> digit_sum(456)

>>> digit_sum(78910)

"""

return sum(int(digit) for digit in str(n))

def solution(n: int = 30) -> int:

"""

Returns the value of 30th digit power sum.

>>> solution(2)

512

>>> solution(5)

5832

>>> solution(10)

614656

"""

digit_to_powers = []

for digit in range(2, 100):

for power in range(2, 100):

number = int(math.pow(digit, power))

if digit == digit_sum(number):

digit_to_powers.append(number)

digit_to_powers.sort()

return digit_to_powers[n - 1]

if __name__ == "__main__":

print(solution())

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