Erdős problem 887 · problems.science

Is there an absolute constant $K$ such that, for every $C > 0$ , if $n$ is sufficiently large then $n$ has at most $K$ divisors in $(n^{\frac{1}{2}}, n^{\frac{1}{2}} + C n^{\frac{1}{4}})$ .

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4 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

887.lean

Retained formal statement3 of 4

Erdős and Rosenfeld, ask whether $4$ is the best possible $K$ for the infinitude of $n$ with (at least) $K$ divisors in $(n^{\frac{1}{2}}, n^{\frac{1}{2}} + n^{\frac{1}{4}})$ .

FormalConjectures/ErdosProblems/887.leanErdos887.erdos_887.variants.rosenfeld_41 lineExact file

1IsGreatest {K | ∃ C > 0, Infinite ↑{n | K ≤ {d ∈ Finset.Ioo ⌊√↑n⌋₊ ⌈√↑n + C * ↑n ^ (1 / 4)⌉₊ | d ∣ n}.card}} 4

OpenStatement only, no proof

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