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

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FormalConjectures/ErdosProblems/

647.lean

Retained formal statement3 of 4

Erdős says 'it is extremely doubtful' that there are infinitely many such $n$ , and in fact suggests that $lim_{n\to\infty} \max_{m < n}(\tau(m) + m − n) = \infty.$

FormalConjectures/ErdosProblems/647.leanErdos647.erdos_647.variants.lim1 lineExact file

1sorry ↔ Filter.Tendsto (fun n => ⨆ m, (ArithmeticFunction.sigma 0) ↑m + ↑m - n) Filter.atTop Filter.atTop

OpenStatement only, no proof

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