# We generate all the possible powers in the given range, put each value
# into a set, and let the set count the number of unique values present.


def problem029():
    """


    Consider all integer combinations of a^b 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?
    """
    seen = set(a ** b for a in range(2, 101) for b in range(2, 101))
    return len(seen)


if __name__ == "__main__":
    print(problem029())
