euler/e029.py

# -*- coding: utf-8 -*-
"""How many distinct terms are in the sequence generated by a**b for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?

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?
"""
MAX = 100

def main():
    numbers = []
    
    for i in range(2, MAX + 1):
        for ii in range(2, MAX + 1):
            n = i**ii
            if n not in numbers:
                numbers.append(n)
    print len(numbers)

if __name__ == '__main__':
    main()