"""
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?


Answer:
    9183
"""


def distinct_powers(a_min, a_max, b_min, b_max):
    return len(set(a**b
                   for a in range(a_min, a_max + 1)
                   for b in range(b_min, b_max + 1)))


def test_0029_distinct_powers():
    assert distinct_powers(2, 100, 2, 100) == 9183
