Erdős problem 647 · problems.science

Let $\tau(n)$ count the number of divisors of $n$ . Is there some $n > 24$ such that $\max_{m < n}(m + \tau(m)) \leq n + 2?$

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4 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

647.lean

Retained formal statement2 of 4

Erdős says it 'seems certain' that for every $k$ there are infinitely many $n$ for which $\max_{n−k < m < n}(m + \tau(m)) ≤ n + 2.$

FormalConjectures/ErdosProblems/647.leanErdos647.erdos_647.variants.infinite1 lineExact file

1sorry ↔ ∀ (k : ℕ), {n | ⨆ m, ↑m + (ArithmeticFunction.sigma 0) ↑m ≤ n + 2}.Infinite

OpenStatement only, no proof