Erdős problem 887

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 $(n^{\frac{1}{2}}, n^{\frac{1}{2}} + C n^{\frac{1}{4}})$ .

Sources

The source's own material, retained exactly.

4 retained statements36c6d0fef71a

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

Source providers

Erdős Problems1
locator only
Formal Conjectures4
statement retained
VibeMathed0
not observed here
PLBY Lean proofs0
not observed here
Jayyhk Erdős Lean0
not observed here
William Blair Lean proofs0
not observed here
Erdős AI contributions wiki0
not observed here
GPT-Erdős0
not observed here

Referenced paths

FormalConjectures/
- ErdosProblems/
  - 887.lean4