'''
Problem 029
Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:

2**2=4, 2**3=8, 2**4=16, 2**5=32
3**2=9, 3**3=27, 3**4=81, 3**5=243
4**2=16, 4**3=64, 4**4=256, 4**5=1024
5**2=25, 5**3=125, 5**4=625, 5**5=3125

If they are then placed in numerical order, with any repeats removed, 
   we get the following sequence of 15 distinct terms:

4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125

How many distinct terms are in the sequence generated by 
   a**b for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100? 


Solution: Copyright 2017 Dave Cuthbert, MIT License
'''


def solve_problem(a,b):
    power_set = set()

    for i in range(2, a + 1):
        for j in range(2, b + 1):
            power_set.add(i ** j)     

    return(len(power_set))


if __name__ == "__main__":
    a = b = 100

    print(solve_problem(a, b))

Solve distinct powers