59 lines
1.8 KiB
Factor
59 lines
1.8 KiB
Factor
! Copyright (c) 2008 Aaron Schaefer.
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! See http://factorcode.org/license.txt for BSD license.
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USING: kernel math math.ranges project-euler.common sequences sets sorting assocs fry ;
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IN: project-euler.023
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! http://projecteuler.net/index.php?section=problems&id=23
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! DESCRIPTION
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! -----------
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! A perfect number is a number for which the sum of its proper divisors is
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! exactly equal to the number. For example, the sum of the proper divisors of
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! 28 would be 1 + 2 + 4 + 7 + 14 = 28, which means that 28 is a perfect number.
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! A number whose proper divisors are less than the number is called deficient
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! and a number whose proper divisors exceed the number is called abundant.
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! As 12 is the smallest abundant number, 1 + 2 + 3 + 4 + 6 = 16, the smallest
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! number that can be written as the sum of two abundant numbers is 24. By
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! mathematical analysis, it can be shown that all integers greater than 28123
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! can be written as the sum of two abundant numbers. However, this upper limit
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! cannot be reduced any further by analysis even though it is known that the
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! greatest number that cannot be expressed as the sum of two abundant numbers
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! is less than this limit.
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! Find the sum of all the positive integers which cannot be written as the sum
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! of two abundant numbers.
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! SOLUTION
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! --------
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! The upper limit can be dropped to 20161 which reduces our search space
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! and every even number > 46 can be expressed as a sum of two abundants
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<PRIVATE
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: source-023 ( -- seq )
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46 [1,b] 47 20161 2 <range> append ;
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: abundants-upto ( n -- seq )
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[1,b] [ abundant? ] filter ;
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: possible-sums ( seq -- seq )
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H{ } clone
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[ dupd '[ _ [ + _ conjoin ] with each ] each ]
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keep keys ;
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PRIVATE>
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: euler023 ( -- answer )
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source-023
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20161 abundants-upto possible-sums diff sum ;
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! [ euler023 ] time
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! 2.15542 seconds
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SOLUTION: euler023
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