Add (slow) Haskell solution for Problem 23

Haskell/p023.hs

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+-- A perfect number is a number for which the sum of its proper divisors is exactly equal to the number.
+-- For example, the sum of the proper divisors of 28 would be 1 + 2 + 4 + 7 + 14 = 28, which means that 28 is a perfect number.
+--
+-- A number n is called deficient if the sum of its proper divisors is less than n and it is called abundant if this sum exceeds n.
+--
+-- As 12 is the smallest abundant number, 1 + 2 + 3 + 4 + 6 = 16, the smallest number that can be written as the sum of two abundant numbers is 24.
+-- By mathematical analysis, it can be shown that all integers greater than 28123 can be written as the sum of two abundant numbers.
+-- However, this upper limit cannot be reduced any further by analysis even though it is known that the greatest number that cannot be expressed
+-- as the sum of two abundant numbers is less than this limit.
+--
+-- Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.
+import Data.List
+
+import ProjectEuler (sumProperDivisors)
+
+isAbundant :: (Integral a) => a -> Bool
+isAbundant n = sumProperDivisors n > n
+
+abundantSums :: (Integral a) => [a]
+abundantSums = nub [ x + y | x <- abundantList, y <- abundantList, x + y <= 28123, y >= x ]
+    where abundantList = [ x | x <- [12..28123], isAbundant x ]
+
+sumNotAbundant :: (Integral a) => a
+sumNotAbundant = sum $ [1..28123] \\ abundantSums
+
+main = do
+    let result = sumNotAbundant
+    putStrLn $ "Project Euler, Problem 23\n"
+        ++ "Answer: " ++ (show result)