The number 81 has a special property, a certain power of the sum of its digits is equal to 81 (nine squared). Eighty one (81), is the first number in having this property (not considering numbers of one digit). 
The next one, is 512.
Let's see both cases with the details

8 + 1 = 9 and 9^(2) = 81

512 = 5 + 1 + 2 = 8 and 8^(3) = 512

We need to make a function, ```power_sumDigTerm()```, that receives a number ```n``` and may output the ```n-th term``` of this sequence of numbers.
The cases we presented above means that

power_sumDigTerm(1) == 81

power_sumDigTerm(2) == 512


Happy coding!

Difficulty: introductory

Starter code:

def power_sumDigTerm(n):
	

Solutions:
series = [0]
for a in range(2, 99):
    for b in range(2, 42):
        c = a**b
        if a == sum(map(int, str(c))):
            series.append(c)
power_sumDigTerm = sorted(series).__getitem__

def dig_sum(n):
    return sum(map(int, str(n)))



terms = []
for b in range(2, 400):
    for p in range(2, 50):
        if dig_sum(b ** p) == b:
            terms.append(b ** p)
terms.sort()

def power_sumDigTerm(n):
    return terms[n - 1]

power_sumDigTerm = [None, 81, 512, 2401, 4913, 5832, 17576, 19683, 234256,
    390625, 614656, 1679616, 17210368, 34012224, 52521875, 60466176, 205962976,
    612220032, 8303765625, 10460353203, 24794911296, 27512614111, 52523350144,
    68719476736, 271818611107, 1174711139837, 2207984167552, 6722988818432,
    20047612231936, 72301961339136, 248155780267521, 3904305912313344,
    45848500718449031, 81920000000000000, 150094635296999121, 13744803133596058624,
    19687440434072265625, 53861511409489970176, 73742412689492826049,
    179084769654285362176, 480682838924478847449].__getitem__

def power_sumDigTerm(n):
    return sorted([i**j for j in range(2,50) for i in range(2,100) if i == sum([int(i) for i in str(i**j) ])])[n-1]

def power_sumDigTerm(n):
    return [81, 512, 2401, 4913, 5832, 17576, 19683, "I'm never tested :(", 390625, 614656, 1679616, 17210368, 34012224, 52521875, 60466176, 205962976, 612220032, 8303765625, 10460353203, 24794911296, 27512614111, 52523350144, 68719476736, 271818611107, 1174711139837, 2207984167552, 6722988818432, 20047612231936, 72301961339136, 248155780267521, 3904305912313344, 45848500718449031, 81920000000000000, 150094635296999121, 13744803133596058624, 19687440434072265625, 53861511409489970176, 73742412689492826049, 39, 40][n-1]

def power_sumDigTerm(n):
    
    def sum_d(x):
        L = [int(d) for d in str(x)]
        res = 0
        for l in L:
            res = res + l
        return res

    r_list = []
    
    for j in range(2, 50):
        for i in range(7, 100): 
            a = i**j
            if sum_d(a) == i:     
                r_list.append(a)
                r_list = list(set(r_list))
                
    r_list = sorted((r_list))
    return r_list[n-1]
                        


def power_sumDigTerm(n):
    my_list=[]
    for number in range(2,100):
        for exponent in range(2,50):
            raised_number=number**exponent
            sum_of_digits=0
            for digit in list(str(raised_number)):
                sum_of_digits+=int(digit)
            if sum_of_digits**exponent==raised_number:
                my_list.append(raised_number)
    answer=sorted(my_list)
    return answer[n-1]

def power_sumDigTerm(n):
    #your code here
    return sorted([a**b for a in range(2, 100) for b in range(2,100) if a == sum(map(int, str(a**b)))])[n-1]

def power_sumDigTerm(n):
    return sorted(set([a**b for a in range(2, 100) for b in range(2,100) if a == sum(map(int, str(a**b)))]))[n-1]