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RichardVasquezRichardVasquez
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Add A000010 Euler's totient sequence (#246)
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‎Algorithms.Tests/Sequences/EulerTotientSequenceTests.cs

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using System.Linq;
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using System.Numerics;
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using Algorithms.Sequences;
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using FluentAssertions;
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using NUnit.Framework;
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namespace Algorithms.Tests.Sequences
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{
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public class EulerTotientSequenceTests
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{
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[Test]
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public void FirstElementsCorrect()
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{
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// Let's be thorough. 500 phi values!
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// Initial test of 69 number from table at https://oeis.org/A000010/list and passed test.
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// Extended out to 500 values from https://primefan.tripod.com/Phi500.html and passed initial 69
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// along with remaining values.
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var check = new BigInteger[]
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{
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1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 4, 12, 6, 8, 8, 16, 6, 18, 8,
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12, 10, 22, 8, 20, 12, 18, 12, 28, 8, 30, 16, 20, 16, 24, 12, 36, 18, 24, 16,
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40, 12, 42, 20, 24, 22, 46, 16, 42, 20, 32, 24, 52, 18, 40, 24, 36, 28, 58, 16,
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60, 30, 36, 32, 48, 20, 66, 32, 44, 24, 70, 24, 72, 36, 40, 36, 60, 24, 78, 32,
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54, 40, 82, 24, 64, 42, 56, 40, 88, 24, 72, 44, 60, 46, 72, 32, 96, 42, 60, 40,
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100, 32, 102, 48, 48, 52, 106, 36, 108, 40, 72, 48, 112, 36, 88, 56, 72, 58, 96, 32,
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110, 60, 80, 60, 100, 36, 126, 64, 84, 48, 130, 40, 108, 66, 72, 64, 136, 44, 138, 48,
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92, 70, 120, 48, 112, 72, 84, 72, 148, 40, 150, 72, 96, 60, 120, 48, 156, 78, 104, 64,
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132, 54, 162, 80, 80, 82, 166, 48, 156, 64, 108, 84, 172, 56, 120, 80, 116, 88, 178, 48,
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180, 72, 120, 88, 144, 60, 160, 92, 108, 72, 190, 64, 192, 96, 96, 84, 196, 60, 198, 80,
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132, 100, 168, 64, 160, 102, 132, 96, 180, 48, 210, 104, 140, 106, 168, 72, 180, 108, 144, 80,
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192, 72, 222, 96, 120, 112, 226, 72, 228, 88, 120, 112, 232, 72, 184, 116, 156, 96, 238, 64,
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240, 110, 162, 120, 168, 80, 216, 120, 164, 100, 250, 72, 220, 126, 128, 128, 256, 84, 216, 96,
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168, 130, 262, 80, 208, 108, 176, 132, 268, 72, 270, 128, 144, 136, 200, 88, 276, 138, 180, 96,
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280, 92, 282, 140, 144, 120, 240, 96, 272, 112, 192, 144, 292, 84, 232, 144, 180, 148, 264, 80,
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252, 150, 200, 144, 240, 96, 306, 120, 204, 120, 310, 96, 312, 156, 144, 156, 316, 104, 280, 128,
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212, 132, 288, 108, 240, 162, 216, 160, 276, 80, 330, 164, 216, 166, 264, 96, 336, 156, 224, 128,
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300, 108, 294, 168, 176, 172, 346, 112, 348, 120, 216, 160, 352, 116, 280, 176, 192, 178, 358, 96,
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342, 180, 220, 144, 288, 120, 366, 176, 240, 144, 312, 120, 372, 160, 200, 184, 336, 108, 378, 144,
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252, 190, 382, 128, 240, 192, 252, 192, 388, 96, 352, 168, 260, 196, 312, 120, 396, 198, 216, 160,
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400, 132, 360, 200, 216, 168, 360, 128, 408, 160, 272, 204, 348, 132, 328, 192, 276, 180, 418, 96,
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420, 210, 276, 208, 320, 140, 360, 212, 240, 168, 430, 144, 432, 180, 224, 216, 396, 144, 438, 160,
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252, 192, 442, 144, 352, 222, 296, 192, 448, 120, 400, 224, 300, 226, 288, 144, 456, 228, 288, 176,
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460, 120, 462, 224, 240, 232, 466, 144, 396, 184, 312, 232, 420, 156, 360, 192, 312, 238, 478, 128,
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432, 240, 264, 220, 384, 162, 486, 240, 324, 168, 490, 160, 448, 216, 240, 240, 420, 164, 498, 200,
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};
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var sequence = new EulerTotientSequence().Sequence.Take(check.Length);
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sequence.SequenceEqual(check).Should().BeTrue();
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}
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}
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}

‎Algorithms/Sequences/EulerTotientSequence.cs

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using System.Collections.Generic;
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using System.Linq;
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using System.Numerics;
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namespace Algorithms.Sequences
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{
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/// <summary>
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/// <para>
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/// Sequence of Euler totient function phi(n).
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/// </para>
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/// <para>
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/// Wikipedia: https://en.wikipedia.org/wiki/Euler%27s_totient_function.
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/// </para>
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/// <para>
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/// OEIS: https://oeis.org/A000010.
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/// </para>
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/// </summary>
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public class EulerTotientSequence : ISequence
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{
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/// <summary>
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/// <para>
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/// Gets sequence of Euler totient function phi(n).
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/// </para>
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/// <para>
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/// 'n' is copied from value of the loop of i that's being enumerated over.
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/// 1) Initialize result as n
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/// 2) Consider every number 'factor' (where 'factor' is a prime divisor of n).
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/// If factor divides n, then do following
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/// a) Subtract all multiples of factor from 1 to n [all multiples of factor
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/// will have gcd more than 1 (at least factor) with n]
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/// b) Update n by repeatedly dividing it by factor.
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/// 3) If the reduced n is more than 1, then remove all multiples
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/// of n from result.
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/// </para>
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/// <para>
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/// Base code was from https://www.geeksforgeeks.org/eulers-totient-function/.
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/// </para>
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/// <para>
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/// Implementation avoiding floating point operations was used for base
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/// and replacement of loop going from 1 to sqrt(n) was replaced with
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/// List of prime factors.
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/// </para>
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/// </summary>
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public IEnumerable<BigInteger> Sequence
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{
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get
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{
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yield return BigInteger.One;
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for (BigInteger i = 2; ; i++)
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{
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var n = i;
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var result = n;
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var factors = PrimeFactors(i);
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foreach (var factor in factors)
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{
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while (n % factor == 0)
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{
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n /= factor;
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}
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result -= result / factor;
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}
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if (n > 1)
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{
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result -= result / n;
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}
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yield return result;
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}
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}
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}
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/// <summary>
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/// <para>
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/// Uses the prime sequence to find all prime factors of the
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/// number we're looking at.
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/// </para>
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/// <para>
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/// The prime sequence is examined until its value squared is
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/// less than or equal to target, and checked to make sure it
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/// evenly divides the target. If it evenly divides, it's added
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/// to the result which is returned as a List.
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/// </para>
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/// </summary>
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/// <param name="target">Number that is being factored.</param>
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/// <returns>List of prime factors of target.</returns>
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private static IEnumerable<BigInteger> PrimeFactors(BigInteger target)
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{
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return new PrimesSequence()
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.Sequence.TakeWhile(prime => prime * prime <= target)
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.Where(prime => target % prime == 0)
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.ToList();
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}
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}
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}

‎README.md

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* [A000004 Zero](./Algorithms/Sequences/ZeroSequence.cs)
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* [A000005 Count of Divisors](./Algorithms/Sequences/DivisorsCountSequence.cs)
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* [A000008 Make Change](./Algorithms/Sequences/MakeChangeSequence.cs)
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* [A000010 Euler's Totient](./Algorithms/Sequences/EulerTotientSequence.cs)
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* [A000027 Natural](./Algorithms/Sequences/NaturalSequence.cs)
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* [A000040 Primes](./Algorithms/Sequences/PrimesSequence.cs)
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* [A000045 Fibonacci](./Algorithms/Sequences/FibonacciSequence.cs)

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