Data update

Task/Arithmetic-numbers/REXX/arithmetic-numbers-1.rexx

@@ -39,7 +39,7 @@ procedure expose divi.
 arg x
 /* Cf definition */
 s = Sigma(x)
-if Iswhole(s/divi.0) then
+if Whole(s/divi.0) then
    return 1
 else
    return 0

Task/Arithmetic-numbers/REXX/arithmetic-numbers-2.rexx

@@ -0,0 +1,76 @@
+parse Version version
+say version; say 'Arithmetic numbers'; say
+Call time 'R'
+numeric digits 9
+a = 0; c = 0
+do i = 1
+/* Is the number arithmetic? */
+   if Arithmetic(i) then do
+      a = a+1
+/* Is the number composite? */
+      if divi.0 > 2 then
+         c = c+1
+/* Output control */
+      if a <= 100 then do
+         if a = 1 then
+            say 'First 100 arithmetic numbers are'
+         call Charout ,Right(i,4)
+         if a//10 = 0 then
+            say
+         if a = 100 then
+            say
+      end
+      if a = 100 | a = 1000 | a = 10000 | a = 100000 | a = 1000000 then do
+         say 'The' a'th arithmetic number is' i
+         say 'Of the first' a 'numbers' c 'are composite'
+         say
+      end
+/* Max 1m, higher takes too long */
+      if a = 1000000 then
+         leave
+   end
+end
+say Format(Time('e'),,3) 'seconds'
+exit
+
+Arithmetic:
+/* Is a number arithmetic? function */
+procedure expose divi.
+arg x
+/* Cf definition */
+s = Sigma(x)
+if Whole(s/divi.0) then
+   return 1
+else
+   return 0
+
+Sigma:
+/* Sigma = Sum of all divisors of x including 1 and x */
+procedure expose divi.
+arg xx
+/* Fast values */
+if xx = 1 then do
+   divi.0 = 1
+   return 1
+end
+/* Euclid's method */
+m = xx//2; yy = 1+xx; n = 2
+do j = 2+m by 1+m while j*j < xx
+   if xx//j = 0 then do
+      yy = yy+j+xx%j; n = n+2
+   end
+end
+if j*j = xx then do
+   yy = yy+j; n = n+1
+end
+/* Store number of divisors */
+divi.0 = n
+/* Return sum */
+return yy
+
+Whole:
+/* Is a number integer? */
+procedure
+arg xx
+/* Formula */
+return Datatype(xx,'w')