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()