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28 lines
935 B
Python
28 lines
935 B
Python
# -*- coding: utf-8 -*-
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"""How many distinct terms are in the sequence generated by a**b for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?
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Consider all integer combinations of a**b for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:
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2**2=4, 2**3=8, 2**4=16, 2**5=32
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3**2=9, 3**3=27, 3**4=81, 3**5=243
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4**2=16, 4**3=64, 4**4=256, 4**5=1024
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5**2=25, 5**3=125, 5**4=625, 5**5=3125
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If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:
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4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125
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How many distinct terms are in the sequence generated by a**b for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?
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"""
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MAX = 100
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def main():
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numbers = []
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for i in range(2, MAX + 1):
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for ii in range(2, MAX + 1):
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n = i**ii
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if n not in numbers:
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numbers.append(n)
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print len(numbers)
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if __name__ == '__main__':
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main()
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