module _23

let abundantUpperLimit = 28123

let abundantNumbers =
    let dSums = 
        common.divisors abundantUpperLimit
        |> Array.mapi (fun i divisors -> (i,  List.fold (+) 0 divisors))
    dSums |> Array.choose ( fun (i, dSum) -> 
        match dSum with
        | abundant when dSum > i -> Some(i)
        | _ -> None
        )

let sumNotAbundant = 
    let a = abundantNumbers
    // add all abubundant numbers together
    
    let sums = common.crossMap (+) a a |> Seq.distinct |> Seq.toArray

    let sna = 
        sums
        |> Set.ofSeq
        |> (-) (Set.ofList [1..abundantUpperLimit])
        |> Set.toSeq
        //|> Array.rev

    sna |> Seq.fold (+) 0