Data update

Task/M-bius-function/C-sharp/m-bius-function.cs

@@ -0,0 +1,84 @@
+using System;
+
+namespace MobiusDemo
+{
+    class Program
+    {
+        // -----------------------------------------------------------------
+        //  Settings that are identical to the Java version
+        // -----------------------------------------------------------------
+        private const int MU_MAX = 1_000_000;   // same upper bound
+        private static int[] MU = null;        // will hold the sieve
+
+        static void Main(string[] args)
+        {
+            Console.WriteLine("First 199 terms of the möbius function are as follows:");
+            Console.Write("    ");
+
+            for (int n = 1; n < 200; n++)
+            {
+                Console.Write($"{MobiusFunction(n),2}  ");
+
+                // line‑break after every 20 numbers – exactly like the Java code
+                if ((n + 1) % 20 == 0)
+                    Console.WriteLine();
+            }
+        }
+
+        // -----------------------------------------------------------------
+        //  Compute μ(n) using the same sieve algorithm that the Java code
+        //  uses. The first call builds the whole table up to MU_MAX.
+        // -----------------------------------------------------------------
+        private static int MobiusFunction(int n)
+        {
+            // If the sieve has already been built we can return the answer
+            // straight away.
+            if (MU != null)
+                return MU[n];
+
+            // -------------------------------------------------------------
+            //  Build the sieve (once)
+            // -------------------------------------------------------------
+            MU = new int[MU_MAX + 1];
+
+            // initialise every entry with 1 – Java did this explicitly
+            for (int i = 0; i <= MU_MAX; i++)
+                MU[i] = 1;
+
+            int sqrt = (int)Math.Sqrt(MU_MAX);
+
+            // first pass: multiply by -p for each prime factor p,
+            // and mark multiples of p² as zero.
+            for (int i = 2; i <= sqrt; i++)
+            {
+                if (MU[i] == 1)                // i is still “prime”
+                {
+                    // flip the sign for every multiple of i
+                    for (int j = i; j <= MU_MAX; j += i)
+                        MU[j] *= -i;
+
+                    // any number that contains i² gets value 0
+                    int i2 = i * i;
+                    for (int j = i2; j <= MU_MAX; j += i2)
+                        MU[j] = 0;
+                }
+            }
+
+            // second pass: reduce the encoded values to the final μ(n)
+            for (int i = 2; i <= MU_MAX; i++)
+            {
+                if (MU[i] == i)          // only +i  => μ = +1
+                    MU[i] = 1;
+                else if (MU[i] == -i)    // only -i  => μ = -1
+                    MU[i] = -1;
+                else if (MU[i] < 0)      // product of an odd number of distinct primes
+                    MU[i] = 1;
+                else if (MU[i] > 0)      // product of an even number of distinct primes
+                    MU[i] = -1;
+                // note: MU[i] == 0 stays 0 (square factor present)
+            }
+
+            return MU[n];
+        }
+    }
+}