From a689f0df146a95559ef4d4ff135db1f740f22346 Mon Sep 17 00:00:00 2001
From: Daniele Fucini <dfucini@gmail.com>
Date: Sat, 9 Nov 2024 22:19:21 +0100
Subject: [PATCH] Add Haskell solutions for Problem 21

---
 Haskell/ProjectEuler.hs |  4 ++++
 Haskell/p021.hs         | 23 +++++++++++++++++++++++
 2 files changed, 27 insertions(+)
 create mode 100644 Haskell/p021.hs

diff --git a/Haskell/ProjectEuler.hs b/Haskell/ProjectEuler.hs
index e3e2b69..7741a1a 100644
--- a/Haskell/ProjectEuler.hs
+++ b/Haskell/ProjectEuler.hs
@@ -1,6 +1,7 @@
 module ProjectEuler
 ( isPrime
 , digitSum
+, sumProperDivisors
 ) where
 
 import Data.Char (digitToInt)
@@ -18,3 +19,6 @@ isPrime n =
 digitSum :: (Integral a, Show a) => a -> Int
 digitSum n = sum $ map digitToInt $ show n
 
+
+sumProperDivisors :: (Integral a) => a -> a
+sumProperDivisors n = sum [ if x /= y then x + y  else x | x <- [2..ceiling $ sqrt $ fromIntegral n], let y = n `div` x, n `mod` x == 0 ] + 1
diff --git a/Haskell/p021.hs b/Haskell/p021.hs
new file mode 100644
index 0000000..23360c4
--- /dev/null
+++ b/Haskell/p021.hs
@@ -0,0 +1,23 @@
+-- Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).
+-- If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and each of a and b are called amicable numbers.
+--
+-- For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284.
+-- The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.
+--
+-- Evaluate the sum of all the amicable numbers under 10000.
+
+import ProjectEuler (sumProperDivisors)
+
+properDivisors :: (Integral a) => a -> [a]
+properDivisors n = [ x | x <- [1..n-1], n `mod` x == 0]
+
+amicable :: (Integral a) => a -> a -> Bool
+amicable x y = x /= y && (sumProperDivisors x) == y && (sumProperDivisors y) == x
+
+sumAmicable :: (Integral a) => a -> a
+sumAmicable n = sum [ x | x <- [1..n-1], amicable x $ sumProperDivisors x ]
+
+main = do
+    let result = sumAmicable 10000
+    putStrLn $ "Project Euler, Problem 21\n"
+        ++ "Answer: " ++ (show result)