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def main():

"""

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?

"""

collectPowers = set()

currentPow = 0

N = 101 # maximum limit

for a in range(2, N):

for b in range(2, N):

currentPow = a**b # calculates the current power

collectPowers.add(currentPow) # adds the result to the set

print("Number of terms ", len(collectPowers))

if __name__ == '__main__':

main()

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