Initial commit.

PerfectNumbers.Core/AlphaCalculations.cs

@@ -0,0 +1,29 @@
+using PeterO.Numbers;
+
+namespace PerfectNumbers.Core;
+
+public static class AlphaCalculations
+{
+    public static ERational ComputeAlphaP(EInteger p, int k)
+    {
+        int exponent = checked(4 * k + 1);
+        EInteger y = PowerCache.Get(p, exponent);
+        return ERational.Create(y * p - 1, y * (p - 1));
+    }
+
+    public static ERational ComputeAlphaFactor(EInteger q, int a2)
+    {
+        EInteger num = PowerCache.Get(q, a2 + 1) - EInteger.One;
+        EInteger den = PowerCache.Get(q, a2) * (q - EInteger.One);
+        return ERational.Create(num, den);
+    }
+
+    public static ERational ComputeAlphaM(ReadOnlySpan<EInteger> primes, int maxR, int a2)
+    {
+        ERational result = ERational.One;
+        for (int i = 0; i < maxR; i++)
+            result = result.Multiply(ComputeAlphaFactor(primes[i], a2));
+        return result;
+    }
+}
+