0029-base-exponent-distinct.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 ab for 2 <= a <= 100 and 2 <= b <= 100?
"""
def the_old_fashioned_way():
    terms = set()
    start = 2
    limit = 100
    for i in range(start, limit + 1):
        for j in range(start, limit + 1):
            answer = i**j
            terms.add(answer)
    ans = len(terms)
    return ans

print "Answer the old-fashioned way:", the_old_fashioned_way()