Problem12.fs

#light
 
(*
    Problem 12: Deep Thought Edition
*)
open System
open System.Collections.Generic
open Microsoft.FSharp.Math
 
let N =
    Seq.unfold (fun x -> Some(x, x + 1I)) 1I
    
let triangleNumbers =
    N |> Seq.map (fun x -> Seq.take_while (fun y -> y <= x) N
                           |> Seq.sum)

let sqrtI = BigInt.ToDouble >> sqrt >> ceil >> string >> BigInt.Parse

let factors n =
    let max = sqrtI n
    Seq.take_while (fun x -> x <= max) N
    |> Seq.filter (fun x -> n % x = 0I)
    |> Seq.map (fun x -> match n with
                         | _ when x = max -> (x, x)
                         | _ -> (x, n / x))
    
let firstTriangleNumberWith_n_Divisors n =
    triangleNumbers
    |> Seq.first (fun x -> let fs = factors x
                           match Seq.length (fs) with
                           | y when y >= n / 2 -> Some(x, fs)
                           | _ -> None)