Solution to Project Euler problem 21

extra/project-euler/016/016.factor

@@ -1,6 +1,6 @@
 ! Copyright (c) 2007 Aaron Schaefer.
 ! See http://factorcode.org/license.txt for BSD license.
-USING: kernel math.functions math.parser sequences ;
+USING: kernel math.functions math.parser project-euler.common sequences ;
 IN: project-euler.016
 
 ! http://projecteuler.net/index.php?section=problems&id=16
@@ -17,7 +17,7 @@ IN: project-euler.016
 ! --------
 
 : euler016 ( -- answer )
-    2 1000 ^ number>string string>digits sum ;
+    2 1000 ^ number>digits sum ;
 
 ! [ euler016 ] 100 ave-time
 ! 0 ms run / 0 ms GC ave time - 100 trials

extra/project-euler/020/020.factor

@@ -1,6 +1,6 @@
 ! Copyright (c) 2007 Aaron Schaefer.
 ! See http://factorcode.org/license.txt for BSD license.
-USING: kernel math.combinatorics math.parser sequences ;
+USING: kernel math.combinatorics math.parser project-euler.common sequences ;
 IN: project-euler.020
 
 ! http://projecteuler.net/index.php?section=problems&id=20
@@ -17,7 +17,7 @@ IN: project-euler.020
 ! --------
 
 : euler020 ( -- answer )
-    100 factorial number>string string>digits sum ;
+    100 factorial number>digits sum ;
 
 ! [ euler020 ] 100 ave-time
 ! 0 ms run / 0 ms GC ave time - 100 trials

extra/project-euler/021/021.factor

@@ -0,0 +1,46 @@
+! 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
+! --------
+
+<PRIVATE
+
+: d ( n -- sum )
+    dup sqrt >fixnum 2 swap [a,b] [
+        [ 2dup divisor? [ 2dup / + , ] [ drop ] if ] each drop
+    ] { } make sum 1+ ;
+
+: amicable-pair? ( n m -- ? )
+    { [ 2dup = not ] [ 2dup d = ] } && 2nip ;
+
+PRIVATE>
+
+: euler021 ( -- answer )
+    10000 [1,b] [ dup dup d amicable-pair? [ drop 0 ] unless ] sigma ;
+
+! [ euler021 ] 100 ave-time
+! 328 ms run / 10 ms GC ave time - 100 trials
+
+MAIN: euler021

extra/project-euler/common/common.factor

@@ -15,6 +15,9 @@ IN: project-euler.common
 : shift-3rd ( seq obj obj -- seq obj obj )
     rot 1 tail -rot ;
 
+: max-children ( seq -- seq )
+    [ dup length 1- [ over nth-pair max , ] each ] { } make nip ;
+
 : >multiplicity ( seq -- seq )
     dup prune [
         [ 2dup [ = ] curry count 2array , ] each
@@ -23,12 +26,6 @@ IN: project-euler.common
 : reduce-2s ( n -- r s )
     dup even? [ factor-2s >r 1+ r> ] [ 1 swap ] if ;
 
-: tau-limit ( n -- n )
-    sqrt floor >fixnum ;
-
-: max-children ( seq -- seq )
-    [ dup length 1- [ over nth-pair max , ] each ] { } make nip ;
-
 PRIVATE>
 
 : collect-consecutive ( seq width -- seq )
@@ -46,8 +43,11 @@ PRIVATE>
         first first
     ] if ;
 
+: number>digits ( n -- seq )
+    number>string string>digits ;
+
 : perfect-square? ( n -- ? )
-    dup sqrt mod zero? ;
+    dup sqrt divisor? ;
 
 : prime-factorization ( n -- seq )
     [
@@ -68,6 +68,7 @@ PRIVATE>
 
 ! Optimized brute-force, is often faster than prime factorization
 : tau* ( n -- n )
-    reduce-2s [ perfect-square? -1 0 ? ] keep dup tau-limit [1,b] [
+    reduce-2s [ perfect-square? -1 0 ? ] keep
+    dup sqrt >fixnum [1,b] [
         dupd divisor? [ >r 2 + r> ] when
     ] each drop * ;

extra/project-euler/project-euler.factor

@@ -1,13 +1,13 @@
 ! Copyright (c) 2007 Aaron Schaefer.
 ! See http://factorcode.org/license.txt for BSD license.
 USING: io io.files kernel math.parser namespaces sequences strings
-    vocabs vocabs.loader system project-euler.ave-time
+    vocabs vocabs.loader system project-euler.ave-time project-euler.common
     project-euler.001 project-euler.002 project-euler.003 project-euler.004
     project-euler.005 project-euler.006 project-euler.007 project-euler.008
     project-euler.009 project-euler.010 project-euler.011 project-euler.012
     project-euler.013 project-euler.014 project-euler.015 project-euler.016
     project-euler.017 project-euler.018 project-euler.019 project-euler.020
-    project-euler.067 ;
+    project-euler.021 project-euler.067 ;
 IN: project-euler
 
 <PRIVATE
@@ -17,7 +17,7 @@ IN: project-euler
     print readln string>number ;
 
 : number>euler ( n -- str )
-    number>string string>digits 3 0 pad-left [ number>string ] map concat ;
+    number>digits 3 0 pad-left [ number>string ] map concat ;
 
 : solution-path ( n -- str )
     number>euler dup [