Euler Totient by Factorization in C#

using System;
// Euler Totient by Factorization in C#
//
// PURPOSE
// Euler totient counts positive integers up to n that are coprime with n.
//
// METHOD
// For each distinct prime divisor p, remove all factors p from a working value and replace
// result with result-result/p. Handle any remaining prime factor.
//
// COMPLEXITY
// O(sqrt(n)) trial-division time and O(1) space.
//
// CONTRACT
// n >= 1. phi(1)=1.
// Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex
// counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers.
// Sorted order, correct tree topology, and caller-owned data-structure invariants are
// preconditions; checking them on every query would change query complexity.
// Scalar and shape checks are included. Value-range checks are included where needed to
// prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000
// workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python
// uses arbitrary precision. Native allocation failures propagate. In-place outputs may be
// partly updated after arithmetic failure. These are single-threaded, in-memory
// implementations.
//
// LANGUAGE DETAILS
// C# / .NET 10: ReadOnlySpan<int> inputs, Span<int> outputs, primitive workspace arrays,
// Array.BinarySearch for LIS, and checked integer arithmetic. Invalid arguments and overflow
// throw exceptions.
//
// EXAMPLE
// Expected return: 6.
// Run: Use Program.cs in a net10.0 console project; dotnet run.
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

class Program {
    static void alg_require(bool valid) { if (!valid) throw new ArgumentException("invalid algorithm input"); }
    static int alg_size(int n) { alg_require(n>=0 && n<=4000000); return n; }

    static int totient(int n) {
        checked {
            alg_require((n >= 1));
            int result = n;
            int p = 2;
            while ((p <= (n / p))) {
                if (((n % p) == 0)) {
                    while (((n % p) == 0)) {
                        n = (n / p);
                    }
                    result = (result - (result / p));
                }
                p = (p + 1);
            }
            if ((n > 1)) {
                result = (result - (result / n));
            }
            return result;
        }
    }

    static void Main() {
        int n = 9;
        int result = totient(n);
        Console.WriteLine(result);
    }
}