Hacktoberfest: project euler solution 119

Name: Digit power sum

Problem Statement: The number 512 is interesting because it is equal to the sum of its digits raised to some power: 5 + 1 + 2 = 8, and 83 = 512. Another example of a number with this property is 614656 = 284.
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

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

reference: #2695

Author: Ravi Kandasamy Sundaram

Diff for: project_euler/problem_119/__init__.py

@@ -0,0 +1,44 @@
+"""
+"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 83 = 512. Another example of a number
+with this property is 614656 = 284. 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
+    """
+    sum = 0
+    while n > 0:
+        sum += n % 10
+        n //= 10
+    return sum
+
+
+def solution() -> int:
+    """
+    Returns the value of a30
+    """
+    powers = []
+    for i in range(2, 100):
+        for j in range(2, 100):
+            n = int(math.pow(i, j))
+            if i == digit_sum(n):
+                powers.append(n)
+
+    powers.sort()
+    return powers[29]
+
+
+if __name__ == "__main__":
+    print(solution())