39 lines
1.1 KiB
Factor
39 lines
1.1 KiB
Factor
! Copyright (c) 2007 Aaron Schaefer.
|
|
! See http://factorcode.org/license.txt for BSD license.
|
|
USING: combinators.lib kernel math math.functions math.ranges namespaces
|
|
project-euler.common sequences ;
|
|
IN: project-euler.021
|
|
|
|
! http://projecteuler.net/index.php?section=problems&id=21
|
|
|
|
! DESCRIPTION
|
|
! -----------
|
|
|
|
! Let d(n) be defined as the sum of proper divisors of n (numbers less than n
|
|
! which divide evenly into n).
|
|
|
|
! 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.
|
|
|
|
! For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44,
|
|
! 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4,
|
|
! 71 and 142; so d(284) = 220.
|
|
|
|
! Evaluate the sum of all the amicable numbers under 10000.
|
|
|
|
|
|
! SOLUTION
|
|
! --------
|
|
|
|
: amicable? ( n -- ? )
|
|
dup sum-proper-divisors
|
|
{ [ 2dup = not ] [ 2dup sum-proper-divisors = ] } && 2nip ;
|
|
|
|
: euler021 ( -- answer )
|
|
10000 [1,b] [ dup amicable? [ drop 0 ] unless ] sigma ;
|
|
|
|
! [ euler021 ] 100 ave-time
|
|
! 328 ms run / 10 ms GC ave time - 100 trials
|
|
|
|
MAIN: euler021
|