problem_029.py

# coding: utf-8

'''
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?
'''


def result(_max):
    memo = set([])
    for a in range(2, _max + 1):
        for b in range(2, _max + 1):
            power = a ** b
            if power not in memo:
                memo.add(power)
    return len(memo)


def test_result():
    assert result(5) == 15


def main():
    return result(100)


if __name__ == '__main__':
    test_result()
    print(main())
    # 9183 in 7.84ms