problem29.py

"""
Distinct Powers
Project Euler Problem #29
by Muaz Siddiqui

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?
"""
def distinct_power(n):
    powers = []
    for a in range(2, n + 1):
        for b in range(2, n + 1):
            next = a ** b
            if next not in powers:
                powers.append(next)
    return len(powers)

def answer():
    return distinct_power(100)