Erdős Problem 248

References:

• erdosproblems.com/248
• [TaTe25] T. Tao and J. Teräväinen, Quantitative correlations and some problems on prime factors of consecutive integers. arXiv:2512.01739 (2025).

theorem Erdos248.erdos_248 : ∃ C > 0, {n : ℕ | ∀ k ≥ 1, ↑(ArithmeticFunction.cardDistinctFactors (n + k)) ≤ C * ↑k}.Infinite

Are there infinitely many $n$ such that $\omega(n + k) \ll k$ for all $k \geq 1$? Here $\omega(n)$ is the number of distinct prime divisors of $n$.