1 ! Copyright (c) 2008 Aaron Schaefer.
2 ! See http://factorcode.org/license.txt for BSD license.
3 USING: hashtables kernel math math.ranges project-euler.common sequences
7 ! http://projecteuler.net/index.php?section=problems&id=23
12 ! A perfect number is a number for which the sum of its proper divisors is
13 ! exactly equal to the number. For example, the sum of the proper divisors of
14 ! 28 would be 1 + 2 + 4 + 7 + 14 = 28, which means that 28 is a perfect number.
16 ! A number whose proper divisors are less than the number is called deficient
17 ! and a number whose proper divisors exceed the number is called abundant.
19 ! As 12 is the smallest abundant number, 1 + 2 + 3 + 4 + 6 = 16, the smallest
20 ! number that can be written as the sum of two abundant numbers is 24. By
21 ! mathematical analysis, it can be shown that all integers greater than 28123
22 ! can be written as the sum of two abundant numbers. However, this upper limit
23 ! cannot be reduced any further by analysis even though it is known that the
24 ! greatest number that cannot be expressed as the sum of two abundant numbers
25 ! is less than this limit.
27 ! Find the sum of all the positive integers which cannot be written as the sum
28 ! of two abundant numbers.
34 ! The upper limit can be dropped to 20161 which reduces our search space
35 ! and every even number > 46 can be expressed as a sum of two abundants
39 : source-023 ( -- seq )
40 46 [1,b] 47 20161 2 <range> append ;
42 : abundants-upto ( n -- seq )
43 [1,b] [ abundant? ] subset ;
45 : possible-sums ( seq -- seq )
48 rot append prune swap 1 tail
49 ] each drop natural-sort ;
53 : euler023 ( -- answer )
54 20161 abundants-upto possible-sums source-023 seq-diff sum ;
56 ! TODO: solution is still too slow, although it takes under 1 minute
59 ! 52780 ms run / 3839 ms GC