The Problem

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?

The Solution

Unless you're working in assembly language, this problem is pretty trivial. It almost seems designed for a functional language with a focus on pipelines. Fortunately for us, we're working with one of those.

Here's the solution in all its glory:

• Start by generating a sequence of all possible a,b pairs.
• For each of those, get a^b
• Filter out the duplicates
• Count what we have left

seq {
    for a in 2I..100I do
        for b in 2..100 -> a,b
}
|> Seq.map (fun (a,b) -> pown a b)
|> Seq.distinct
|> Seq.length

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