'''
Consider all integer combinations of ab 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 ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?
'''

# brute force
def distinct_powers(max_a, max_b):
  distinct = {}
  for a in range(2, max_a+1):
    for b in range(2, max_b+1):
      distinct[a**b] = a
  return len(distinct.keys())

distinct_powers(100, 100)
