Exposing the body of perfect? as aliquot.

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

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

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)