problem_29.py

#!/usr/bin/env python
# -*- coding: utf-8 -*-

'''
Problem 29

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?
'''

print len(set(a ** b for a in xrange(2, 101) for b in xrange(2, 101)))