Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:

2^2=4, 2^3=8, 2^4=16, 2^5=32
3^2=9, 3^3=27, 3^4=81, 3^5=243
4^2=16, 4^3=64, 4^4=256, 4^5=1024
5^2=25, 5^3=125, 5^4=625, 5^5=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?



In [46]:

    
open System.Numerics

let a_max = 100
let b_max = 100

let p a b = 
    BigInteger.Pow(a, b)

let solutionsFor (a:int) =    
    [2..b_max]
    |> List.map (p (new BigInteger(a)))
    
[2..a_max]
|> List.map solutionsFor
|> List.concat
|> List.distinct
|> List.length









    Out[46]:





9183