module _12
open System

let fiveDivisorTriangle =
    let root (n : int) = int( Math.Sqrt(float(n)) )
    // observation: if number has a factor < sqrt(num), then it has a corresponding
    //   factor > sqrt(num)
    let factorCount x = Seq.sum (seq { for i = 1 to root x do if x % i = 0 then yield 2 })

    let result =
        (1, 0) |> Seq.unfold (fun (num,acc) -> 
                    Some(num + acc, (num + 1, num + acc)))
                 |> Seq.filter (fun x -> 
                    let factCount = factorCount x
                    factCount >= 500 )
                 |> Seq.head
    result