Dataset: Collatz Stopping Times and Arithmetic Functions for n = 2 to 500,000

Dataset supporting the paper "The Radical of an Integer as an Optimal Predictor of Collatz Stopping Times: An Information-Theoretic Analysis". Contains 499,999 rows (n = 2 to 500,000) with the following columns: - n: the integer - stop_n: total Collatz stopping time (steps to reach 1) - rad_n: radical of n (product of distinct prime factors) - phi_n: Euler's totient function φ(n) - sigma_n: sum of divisors σ(n) - omega_n: number of distinct prime factors ω(n) - Omega_n: number of prime factors with multiplicity Ω(n) - v2_n: 2-adic valuation ν₂(n) Computed using a sieve-based algorithm in PHP. All values are exact integers.