p21.u

floorOfSquareRoot n =
  n
    |> Nat.toFloat
    |> sqrt
    |> floor
    |> unsafeToInt
    |> truncate0

> floorOfSquareRoot 12

divides n m = (Nat.mod n m) == 0

> divides 9 3
> divides 8 3

divisors n =
  (List.rangeClosed 1 (floorOfSquareRoot n))
    |> (List.filter (m -> (divides n m)))
    |> (List.map (m -> [m, n/m]))
    |> List.join
    |> List.distinct

properDivisors n = (List.filter (m -> m != n) (divisors n))

> properDivisors 12
> properDivisors 4

properDivisorSum n = (List.foldLeft (Nat.+) 0 (properDivisors n))

> properDivisorSum 12

nToSum = Map.fromList (List.map (n -> (n, (properDivisorSum n))) (List.range 1 10000))

> Map.get 220 nToSum
> Map.get 284 nToSum

amicablePairs =
  Map.toList nToSum
    |> List.filter (cases (n, sum) -> (n != sum) && (n == (properDivisorSum sum)))

amicableNumbers =
  amicablePairs
    |> List.map (cases (n, sum) -> [n, sum])
    |> List.join
    |> List.distinct

amicableNumbersSum = List.foldLeft (Nat.+) 0 amicableNumbers

> amicableNumbersSum