Project Euler 29: Find the number of distinct terms in the sequence generated by a^b

Problem Description

Consider all integer combinations of a^b 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?

Analysis

Build a set of distinct a^b terms using Python’s set data type and print the set’s length.

Project Euler 29 Solution

Afterthoughts

• Python supports large integers inherently.
  
• The answer for a^b for 2 ≤ a ≤ 200 and 2 ≤ b ≤ 200 is 37,774
  
• and for 2 ≤ a ≤ 1000 and 2 ≤ b ≤ 1000 is 977,358.
  
• Mathematica: Length@Union@Flatten@Table[a^b,{a,2,100},{b,2,100}]