""" Project Eurler 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?
"""
"""
	Theory: This is easy. Just need to get a duplicates free collection of a^b for 2 <= a <= 100 and 2 <= b <= 100, and report the length.
"""

res = set()
for a in range(2, 101):
	for b in range(2, 101):
		res.add(a**b)

print "Number of distinct terms are in the sequence generated by a^b for 2 <= a <= 100 and 2 <= b <= 100: " + str(len(res))