solution.py

def main():
    """ 
    Consider all integer combinations of ab for 2 <= a <= 5 and 2 <= b <= 5:

    22=4, 23=8, 24=16, 25=32
    32=9, 33=27, 34=81, 35=243
    42=16, 43=64, 44=256, 45=1024
    52=25, 53=125, 54=625, 55=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 ab for 2 <= a <= 100 and 2 <= b <= 100?
    """

    collectPowers = set()

    currentPow = 0

    N = 101     # maximum limit

    for a in range(2,N):

        for b in range (2,N):

            currentPow = a**b   # calculates the current power
            collectPowers.add(currentPow)   # adds the result to the set
            

    print "Number of terms ", len(collectPowers)


if __name__ == '__main__':
    main()