Data update

Task/Tau-function/Fennel/tau-function.fennel

@@ -0,0 +1,45 @@
+(do ;;; find the count of the divisors of the first 100 positive integers
+
+    ; returns the number of divisors of v
+    (fn divisor-count [v]
+        (var (total n) (values 1 v))
+        ; Deal with powers of 2 first
+        (while (= 0 (% n 2))
+               (set total (+ total 1))
+               (set n  (math.floor (/ n 2)))
+        )
+        ; Odd prime factors up to the square root
+        (var p 1)
+        (while (do (set p (+ p 2))
+                   (<= (* p p) n)
+               )
+               (var count 1)
+               (while (= 0 (% n p))
+                      (set count (+ count 1))
+                      (set n (math.floor (/ n p)))
+               )
+               (set total (* total count))
+        )
+        ; If n > 1 then it's prime
+        (when (> n 1)
+              (set total (* total 2))
+        )
+        total
+    )
+
+    (do
+        (local limit 100)
+        (io.write (.. "Count of divisors for the first " limit " positive integers:\n"))
+        (for [n 1 limit]
+             (io.write (string.format "%3d%s"
+                                      (divisor-count n)
+                                      (if (= 0 (% n 20))
+                                          "\n"
+                                      ;else
+                                          " "
+                                      )
+                       )
+             )
+        )
+    )
+)