implement Euler's phi function

Author: TilmanNeumann

src/main/java/de/tilman_neumann/jml/Divisors.java

@@ -1,6 +1,6 @@
 /*
  * java-math-library is a Java library focused on number theory, but not necessarily limited to it. It is based on the PSIQS 4.0 factoring project.
- * Copyright (C) 2018-2024 Tilman Neumann - tilman.neumann@web.de
+ * Copyright (C) 2018-2026 Tilman Neumann - tilman.neumann@web.de
  *
  * This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License
  * as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.
@@ -511,4 +511,27 @@ public static BigInteger getBiggestDivisorBelowSqrtN(BigInteger n, SortedMap<Big
     	SortedSet<BigInteger> smallDivisors = getSmallDivisors(n, factors);
     	return smallDivisors.last();
     }
+    
+
+	/**
+	 * Computes Euler's phi(n), which is the number of k with 1<=k<=n that are coprime to n.
+	 * Formula: phi(n) = n * prod_{p|n} 1-1/p
+     *
+	 * @param n
+	 * @return phi(n)
+	 */
+	public static BigInteger computeEulerPhi(BigInteger n) {
+		if (n.equals(I_0)) return I_0;
+		
+		SortedMap<BigInteger, Integer> factors = FactorAlgorithm.getDefault().factor(n);
+		BigInteger num = I_1;
+		BigInteger den = I_1;
+		for (Map.Entry<BigInteger, Integer> entry : factors.entrySet()) {
+			BigInteger divisor = entry.getKey();
+			num = num.multiply(divisor.subtract(I_1));
+			den = den.multiply(divisor);
+		}
+		return n.multiply(num).divide(den);
+	}
+
 }

src/test/java/de/tilman_neumann/jml/DivisorsTest.java

@@ -1,6 +1,6 @@
 /*
  * java-math-library is a Java library focused on number theory, but not necessarily limited to it. It is based on the PSIQS 4.0 factoring project.
- * Copyright (C) 2018-2024 Tilman Neumann - tilman.neumann@web.de
+ * Copyright (C) 2018-2026 Tilman Neumann - tilman.neumann@web.de
  *
  * This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License
  * as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.
@@ -19,6 +19,8 @@
 import java.math.BigInteger;
 import java.util.List;
 
+import org.apache.logging.log4j.LogManager;
+import org.apache.logging.log4j.Logger;
 import org.junit.BeforeClass;
 import org.junit.Test;
 
@@ -31,6 +33,8 @@
  */
 public class DivisorsTest {
 
+	private static Logger LOG = LogManager.getLogger(DivisorsTest.class);
+	
 	@BeforeClass
 	public static void setup() {
 		ConfigUtil.initProject();
@@ -46,4 +50,16 @@ public void testSumOfDivisorsForSmallIntegers() {
 			assertEquals(BigInteger.valueOf(reference.get(i)), Divisors.sumOfDivisors_v1(n));
 		}
 	}
+	
+	@Test
+	public void testEulerPhiForSmallArguments() {
+		// reference data from https://oeis.org/A000010, starts at n=1
+		List<Integer> reference = List.of(1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 4, 12, 6, 8, 8, 16, 6, 18, 8, 12, 10, 22, 8, 20, 12, 18, 12, 28, 8, 30, 16, 20, 16, 24, 12, 36, 18, 24, 16, 40, 12, 42, 20, 24, 22, 46, 16, 42, 20, 32, 24, 52, 18, 40, 24, 36, 28, 58, 16, 60, 30, 36, 32, 48, 20, 66, 32, 44);
+		for (int i=0; i<reference.size(); i++) {
+			BigInteger n = BigInteger.valueOf(i+1);
+			BigInteger phi = Divisors.computeEulerPhi(n);
+			LOG.trace("i=" + i + ": phi = " + phi);
+			assertEquals(BigInteger.valueOf(reference.get(i)), phi);
+		}
+	}
 }