From 1ab7d12b21f72f8ca7980718657499cf9eb4c3e2 Mon Sep 17 00:00:00 2001
From: Alex Shinn <ashinn@users.noreply.github.com>
Date: Tue, 10 Jun 2014 20:07:49 +0900
Subject: [PATCH] Exposing the body of perfect? as aliquot.

---
 lib/chibi/math/prime.scm | 16 ++++++++++------
 lib/chibi/math/prime.sld |  3 ++-
 tests/prime-tests.scm    |  2 ++
 3 files changed, 14 insertions(+), 7 deletions(-)

diff --git a/lib/chibi/math/prime.scm b/lib/chibi/math/prime.scm
index a5d70a39..701d1ef7 100644
--- a/lib/chibi/math/prime.scm
+++ b/lib/chibi/math/prime.scm
@@ -205,15 +205,19 @@
             ((= 1 (gcd n i)) (lp (+ i 1) (+ count 1)))
             (else (lp (+ i 1) count))))))
 
+;;> The aliquot sum s(n), equal to the sum of proper divisors of an
+;;> integer n.
+(define (aliquot n)
+  (let ((limit (+ 1 (quotient n 2))))
+    (let lp ((i 2) (sum 1))
+      (cond ((> i limit) sum)
+            ((zero? (remainder n i)) (lp (+ i 1) (+ sum i)))
+            (else (lp (+ i 1) sum))))))
+
 ;;> Returns true iff \var{n} is a perfect number, i.e. the sum of its
 ;;> divisors other than itself equals itself.
 (define (perfect? n)
-  (and (> n 1)
-       (let ((limit (+ 1 (quotient n 2))))
-         (let lp ((i 2) (sum 1))
-           (cond ((> i limit) (= n sum))
-                 ((zero? (remainder n i)) (lp (+ i 1) (+ sum i)))
-                 (else (lp (+ i 1) sum)))))))
+  (and (> n 1) (= n (aliquot n))))
 
 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
 ;; Random prime generation
diff --git a/lib/chibi/math/prime.sld b/lib/chibi/math/prime.sld
index 1ee9ea45..61474975 100644
--- a/lib/chibi/math/prime.sld
+++ b/lib/chibi/math/prime.sld
@@ -1,7 +1,8 @@
 
 (define-library (chibi math prime)
   (import (scheme base) (scheme inexact) (srfi 27) (srfi 33))
-  (export prime? nth-prime prime-above prime-below factor perfect? totient
+  (export prime? nth-prime prime-above prime-below factor perfect?
+          totient aliquot
           provable-prime? probable-prime?
           random-prime random-prime-distinct-from
           coprime? random-coprime modular-inverse modular-expt
diff --git a/tests/prime-tests.scm b/tests/prime-tests.scm
index 7f3eb66d..540c3ab0 100644
--- a/tests/prime-tests.scm
+++ b/tests/prime-tests.scm
@@ -70,6 +70,8 @@
 (test '(2 2 3) (factor 12))
 (test '(3 3 3 5 7) (factor 945))
 
+(test 975 (aliquot 945))
+
 (do ((i 3 (+ i 2)))
     ((>= i 101))
   (test (number->string i) (prime? i)