(* 
 * A number n is a perfect number if the sum of
 * all its divisors (including itself) equals n
 *)

let fst = fn x => x.1 in
let snd = fn x => x.2 in

let factorize =
  fn (x:int): int * int =>
    if x < 2 then (1, x)
    else (fun g (y) =>
            if y * y > x then (1, x)
            else if x mod y = 0 then (y, x / y) else g(y+1)) (2) in

let sum_of_divisors =
  fun f(x) =>
    let yz = factorize (x) in
    let y = fst (yz) in
    let z = snd (yz) in
    let aux =
      fun aux (Y) (z) =>
          if z mod y = 0 then aux (y * Y) (z / y)
          else ((y * Y - 1) / (y - 1), z) in
    if y = 1 then 1+z
    else let Yz = aux (y) (z) in fst(Yz) * f(snd(Yz)) in

let perfect = (* find the first perfect number larger than or equal to x *)
  fun f(x) =>
    if sum_of_divisors (x) = x + x then x
    else f (x+1) in

perfect (1000)

(* answer is 8128 *)