/extra/project-euler/023/023.factor

 1! Copyright (c) 2008 Aaron Schaefer.
 2! See http://factorcode.org/license.txt for BSD license.
 3USING: kernel math math.ranges project-euler.common sequences sets sorting assocs fry ;
 4IN: project-euler.023
 5
 6! http://projecteuler.net/index.php?section=problems&id=23
 7
 8! DESCRIPTION
 9! -----------
10
11! A perfect number is a number for which the sum of its proper divisors is
12! exactly equal to the number. For example, the sum of the proper divisors of
13! 28 would be 1 + 2 + 4 + 7 + 14 = 28, which means that 28 is a perfect number.
14
15! A number whose proper divisors are less than the number is called deficient
16! and a number whose proper divisors exceed the number is called abundant.
17
18! As 12 is the smallest abundant number, 1 + 2 + 3 + 4 + 6 = 16, the smallest
19! number that can be written as the sum of two abundant numbers is 24. By
20! mathematical analysis, it can be shown that all integers greater than 28123
21! can be written as the sum of two abundant numbers. However, this upper limit
22! cannot be reduced any further by analysis even though it is known that the
23! greatest number that cannot be expressed as the sum of two abundant numbers
24! is less than this limit.
25
26! Find the sum of all the positive integers which cannot be written as the sum
27! of two abundant numbers.
28
29
30! SOLUTION
31! --------
32
33! The upper limit can be dropped to 20161 which reduces our search space
34! and every even number > 46 can be expressed as a sum of two abundants
35
36<PRIVATE
37
38: source-023 ( -- seq )
39    46 [1,b] 47 20161 2 <range> append ;
40
41: abundants-upto ( n -- seq )
42    [1,b] [ abundant? ] filter ;
43
44: possible-sums ( seq -- seq )
45    H{ } clone
46    [ dupd '[ _ [ + _ conjoin ] with each ] each ]
47    keep keys ;
48
49PRIVATE>
50
51: euler023 ( -- answer )
52    source-023
53    20161 abundants-upto possible-sums diff sum ;
54
55! [ euler023 ] time
56! 2.15542 seconds
57
58SOLUTION: euler023