From 3ffc76713f6db4c33f20588ce6896ea3c2bae2a7 Mon Sep 17 00:00:00 2001
From: Charles <sircharlesaze@gmail.com>
Date: Sat, 17 Aug 2019 21:39:43 +0200
Subject: wip directory for each language

---
 haskell/wip/023-non_abundant_sum.hs | 57 +++++++++++++++++++++++++++++++++++++
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 create mode 100644 haskell/wip/023-non_abundant_sum.hs

(limited to 'haskell/wip/023-non_abundant_sum.hs')

diff --git a/haskell/wip/023-non_abundant_sum.hs b/haskell/wip/023-non_abundant_sum.hs
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+-- Non-abundant sums
+--
+-- Problem 23
+-- 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(nub)
+
+main = do
+    -- print (nub [n | n <- [1..28123], a <- abundants, a < n, n - a `notElem` abundants])
+    -- print ([n | n <- [1..2812], notAbundantSum n])
+    print (length filteredMultiples)
+    -- print ([n | n <- filteredMultiples, notAbundantSum n])
+    -- print (combkk
+
+
+
+filteredMultiples = filter (\n -> n `notElem` abundantsMultiples) [1..20161]
+abundantsMultiples = [a * x | a <- abundants, x <- [2..1700], a * x < 20161]
+
+notAbundantSum :: Int -> Bool
+notAbundantSum x
+    | x > 28123= False
+    | otherwise = findAbSum 0
+    where findAbSum i
+            | curr > x - 12 || i == length abundants = True
+            | (x - curr) `elem` abundants = False
+            | otherwise = findAbSum (i + 1)
+            where curr = abundants !! i
+
+abundants = [n | n <- [1..28123], divSum n > n]
+
+divSum :: Int -> Int
+divSum n = factorise 2
+    where factorise d
+            | d > nSqrt = 1
+            | rest == 0 && d /= quotient = d + quotient + factorise (d + 1)
+            | rest == 0 && d == quotient = quotient + factorise (d + 1)
+            | otherwise = factorise (d + 1)
+            where quotient = n `div` d
+                  rest = n `mod` d
+          nSqrt = floor $ sqrt $ fromIntegral n
-- 
cgit