Initial data commit

Task/Tau-function/Lua/tau-function.lua

@@ -0,0 +1,33 @@
+function divisorCount(n)
+    local total = 1
+    -- Deal with powers of 2 first
+    while (n & 1) == 0 do
+        total = total + 1
+        n = math.floor(n / 2)
+    end
+    -- Odd prime factors up tot eh square root
+    local p = 3
+    while p * p <= n do
+        local count = 1
+        while n % p == 0 do
+            count = count + 1
+            n = n / p
+        end
+        total = total * count
+        p = p + 2
+    end
+    -- If n > 1 then it's prime
+    if n > 1 then
+        total = total * 2
+    end
+    return total
+end
+
+limit = 100
+print("Count of divisors for the first " .. limit .. " positive integers:")
+for n=1,limit do
+    io.write(string.format("%3d", divisorCount(n)))
+    if n % 20 == 0 then
+        print()
+    end
+end