#Problem 29

'''
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?'''

numbers=[]

def Main():
  for i in range(2,101):
    for j in range(2,101):
      c=i**j
      if c in numbers:
        continue
      else:
        numbers.append(c)
  # num=numbers.sort() #for a ascending order of elements
  print("Number of distinct terms in the sequence are:",len(numbers))

if __name__=="__main__":
  Main()
  
