Haskell Quiz/Weird Numbers/Solution Dolio

A first, rather naive solution:

module Main where
import Control.Monad.Reader
import Data.List
import System

power = filterM $ const [True,False]

divisors n = sort $ 1 : join [ [x, n `div` x] | x <- l ]
 where l = filter ((==0) . (mod n)) . takeWhile ((<n) . join (*)) $ [2..]

weird n = sum s > n && all (n/=) (map sum ss)
 where (s:ss) = power $ divisors n

main = print . filter weird . enumFromThenTo 70 72 . read . head =<< getArgs

A much more efficient solution, implementing some of the techniques from the rubyquiz discussion:

module Main where
import Control.Monad.Reader
import Data.List
import System

power = filterM $ const [True,False]

divisors n = nub $ 1 : l ++ map (div n) (reverse l)
 where l = filter ((==0) . (mod n)) . takeWhile ((<=n) . join (*)) $ [2..]

weird n
    | a <= 0     = False
    | a `elem` d = False
    | sd == a    = False
    | sd < a     = True
    | otherwise  = checkSubset a d
 where d = divisors n
       sd = sum d
       a = sd - n

checkSubset a [] = True
checkSubset a l@(x:xs)
    | a `seq` False = undefined -- strictness
    | a < 0      = True
    | a `elem` l = False
    | null xs    = True
    | otherwise  = checkSubset (a - x) xs && checkSubset a xs

main = print . filter weird . enumFromThenTo 70 72 . read . head =<< getArgs