Number classification in Haskell

Classifier.hs

data Classification = Perfect | Abundant | Deficient deriving (Eq, Show, Ord)

squareRoot :: Int -> Int
squareRoot = floor . sqrt . fromIntegral

isFactor :: Int -> Int -> Bool
isFactor a b = a `mod` b == 0

factors :: Int -> [Int]
factors n = lowFactors ++ highFactors
    where lowFactors = filter (isFactor n) [1..limit]
          limit = squareRoot n
          highFactors = map (n `div`) lowFactors

classify :: Int -> (Int, Classification)
classify n
    | sumOfFactors == n'  = (n, Perfect)
    | sumOfFactors < n'   = (n, Deficient)
    | sumOfFactors > n'   = (n, Abundant)
    where n' = 2 * n
          sumOfFactors = sum $ factors  n

perfectNumbers = filter (\(n, c) -> c == Perfect) $ map classify [1..]

Nice! Are you planning to use classify for something else where you need the result type to be (Int, Classification)? If not, you could simplify the return type of classify and slightly simplify perfectNumbers.

It was originally just returning the classification, but I wanted the number too....didn't think too hard about it. It's not for anything, I was just watching a talk where he was discussing this algorithm.

Do you have a link to the talk? I'd be interested.

http://www.infoq.com/presentations/Functional-Thinking