labLPL/sumDivisors/Program.fs

open System

let factorsWithMolteplicity n =
  let rec loop c p =
    if c < (p * p) then [c]
    elif c % p = 0 then p :: (loop (c/p) p)
    else loop c (p + 1)
  loop n 2
  |> List.countBy id

let isPerfect n =
  let sumDiv k =
    k
    |> factorsWithMolteplicity
    |> List.map (fun (p,m) -> ((pown p (m+1))-1)/(p-1))
    |> List.fold (*) 1
  sumDiv n = 2*n

// brute-force approach
let divisors n =
    [1..n/2]
    |> Seq.filter (fun f -> n % f = 0)
let sumProperDivisors n =
    n
    |> divisors
    |> Seq.sum

// perfect
let isPerfect2 n = (sumProperDivisors n = n)

let timer = new System.Diagnostics.Stopwatch()
timer.Start()
printfn "%A" (isPerfect 8128)
timer.Stop()
printfn "%f" timer.Elapsed.TotalMilliseconds
printfn "Elapsed Time: %i" timer.ElapsedMilliseconds

let timer2 = new System.Diagnostics.Stopwatch()
timer2.Start()
printfn "%A" (isPerfect2 8128)
timer2.Stop()
printfn "%f" timer2.Elapsed.TotalMilliseconds
printfn "Elapsed Time: %i" timer2.ElapsedMilliseconds