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Problem
The 5-digit number, 16807=75, is also a fifth power. Similarly, the 9-digit number, 134217728=89, is a ninth power.
How many n-digit positive integers exist which are also an nth power?
Solution
let naturalNumbers = Seq.unfold (fun state -> Some(state, state+1)) 1
// define function to find the number of n digit numbers which are also nth power
let f n =
naturalNumbers
|> Seq.map (fun n' -> pown (bigint(n')) n)
|> Seq.skipWhile (fun n' -> n'.ToString().Length < n)
|> Seq.takeWhile (fun n' -> n'.ToString().Length = n)
|> Seq.length
let answer =
naturalNumbers
|> Seq.map f
|> Seq.takeWhile (fun l -> l > 0)
|> Seq.sum
