Project Euler – Problem 29 Solution

Problem

Consider all integer combinations of a^b for $latex 2 \leq a \leq 5 $ and $latex 2 \leq b \leq 5$:

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 $latex 2 \leq a \leq 100$ and $latex 2 \leq b \leq 100$?

Solution

let getCombos a b = [2I..a] |> List.collect (fun x -> [2..b] |> List.map (fun y -> (x, y)))

let answer =
    getCombos 100I 100
    |> List.map (fun (a, b) -> pown a b)
    |> List.sort
    |> Seq.distinct
    |> Seq.length