p029.py

# This Python file uses the following encoding: utf-8

#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?

import logging

def main(args):
    terms = set()
    r = 100
    for a in range(2, r+1):
        for b in range(2, r+1):
            terms.add(a**b)
                
    # print terms
    logging.info(len(terms))