Distinct Powers.py

'''
Problem 29
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?
'''


def getEvenBase():

    evenBasePowers = []

    for exponent in range(2, 101):
        evenBasePowers.append(2**exponent)

    return evenBasePowers

def getOddBase():

    oddBasePowers = []

    for exponent in range(2, 101):
        oddBasePowers.append(3**exponent)

    return oddBasePowers


def main():
    evenBase = getEvenBase()
    oddBase = getOddBase()

    for number in range(4, 101):

        for exponent in range(2, 101):

            power = number**exponent

            if number % 2 == 0:
                if power not in evenBase:
                    evenBase.append(power)
            else:
                if power not in oddBase:
                    oddBase.append(power)

    print(len(evenBase + oddBase))

if __name__ == '__main__':
    main()