Data update

Task/Tau-function/C-sharp/tau-function.cs

@@ -0,0 +1,51 @@
+internal class Program
+{
+    private static void Main(string[] args)
+    {
+        long limit = 100;
+        Console.WriteLine($"Count of divisors for the first {limit} positive integers:");
+        long count = 0;
+
+        for (long n = 1; count < limit; ++n)
+        {
+            Console.Write($"{DivisorCount(n),3} ");
+            ++count;
+
+            if (count % 20 == 0)
+            {
+                Console.WriteLine();
+            }
+        }
+    }
+
+    private static long DivisorCount(long n)
+    {
+        long total = 1;
+        // Deal with powers of 2 first
+        for (; (n & 1) == 0; n >>= 1)
+        {
+            ++total;
+        }
+
+        // Odd prime factors up to the square root
+        for (long p = 3; p * p <= n; p += 2)
+        {
+            long count = 1;
+
+            for (; n % p == 0; n /= p)
+            {
+                ++count;
+            }
+
+            total *= count;
+        }
+
+        // If n > 1 then it's prime
+        if (n > 1)
+        {
+            total *= 2;
+        }
+
+        return total;
+    }
+}