29.py

#! /usr/bin/env python

# 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?


def distinct_powers(a_limit, b_limit):
    results = set()

    for a in range(2, a_limit + 1):
        for b in range(2, b_limit + 1):
            results.add(a ** b)

    return len(results)


print distinct_powers(100, 100)