#! /usr/bin/env python3

description = """
Distinct powers
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 a**b for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?
"""

def distinctTerms(max):
  return sorted(dict((a**b, True) for a in range(2, max+1) for b in range(2, max+1)).keys())

assert([4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125] == distinctTerms(5))

print(len(distinctTerms(100)), 'distinct terms')

83334c0a67ed13b0d480d3437b956d157c6cdeb2
<mask token>

<mask token>


def distinctTerms(max):
    return sorted(dict((a ** b, True) for a in range(2, max + 1) for b in
        range(2, max + 1)).keys())


<mask token>

<mask token>


def distinctTerms(max):
    return sorted(dict((a ** b, True) for a in range(2, max + 1) for b in
        range(2, max + 1)).keys())


assert [4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
    ] == distinctTerms(5)
print(len(distinctTerms(100)), 'distinct terms')

description = """
Distinct powers
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 a**b for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?
"""


def distinctTerms(max):
    return sorted(dict((a ** b, True) for a in range(2, max + 1) for b in
        range(2, max + 1)).keys())


assert [4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
    ] == distinctTerms(5)
print(len(distinctTerms(100)), 'distinct terms')

#! /usr/bin/env python3

description = """
Distinct powers
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 a**b for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?
"""

def distinctTerms(max):
  return sorted(dict((a**b, True) for a in range(2, max+1) for b in range(2, max+1)).keys())

assert([4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125] == distinctTerms(5))

print(len(distinctTerms(100)), 'distinct terms')
