### The Problem

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?

### 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 ab
• 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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