Erdős problem 248

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 $n$ .

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1 retained statement36c6d0fef71a

FormalConjectures/ErdosProblems/

248.lean

Retained formal statement1 of 1

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 $n$ .

FormalConjectures/ErdosProblems/248.leanErdos248.erdos_2481 lineExact file

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

SolvedStatement only, no proof