Erdős problem 647

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

Sources

The source's own material, retained exactly.

4 retained statements36c6d0fef71a

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