24 lines
995 B
Haskell
24 lines
995 B
Haskell
-- Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).
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-- 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.
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--
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-- For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284.
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-- The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.
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--
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-- Evaluate the sum of all the amicable numbers under 10000.
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import ProjectEuler (sumProperDivisors)
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properDivisors :: (Integral a) => a -> [a]
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properDivisors n = [ x | x <- [1..n-1], n `mod` x == 0]
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amicable :: (Integral a) => a -> a -> Bool
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amicable x y = x /= y && sumProperDivisors x == y && sumProperDivisors y == x
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sumAmicable :: (Integral a) => a -> a
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sumAmicable n = sum [ x | x <- [1..n-1], amicable x $ sumProperDivisors x ]
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main = do
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let result = sumAmicable 10000
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putStrLn $ "Project Euler, Problem 21\n"
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++ "Answer: " ++ show result
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