let max = 10000

let prime = Array.create (max + 1) true

prime.[0] <- false

prime.[1] <- false

for i in 2 .. max |> float |> sqrt |> int do

    if prime.[i] then

        for j in i * i .. i .. max do

            prime.[j] <- false

let primes =

    prime

    |> Array.mapi (fun i p -> i, p)

    |> Array.choose (fun (i, p) -> if p then Some i else None)

printfn "%A" primes

let primeDecomp n =

    primes

    |> Seq.takeWhile (fun p -> p <= n)

    |> Seq.filter (fun p -> n % p = 0)

    |> Seq.map (fun p ->

                    let mutable x = 1

                    let mutable n = n

                    while n % p = 0 do

                        x <- x + 1

                        n <- n / p

                    p, x - 1

               )

let divisors n =

    n

    |> primeDecomp

    |> Seq.map (snd >> (+) 1)

    |> Seq.fold (*) 1

for i in 10000 .. 20000 do

    let i = i * (i + 1) / 2

    if divisors i >= 500 then

        printfn "%i" i