Erdős problem 942 · problems.science

Let $h(n)$ count powerful integers in $[n^2, (n+1)^2)$ . What is the extremal order of $h(n)$ ?

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4 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

942.lean

Retained formal statement1 of 3

Is there some constant $c > 0$ such that $h(n) < (\log n)^{c + o(1)}$ and, for infinitely many $n$ , $h(n) > (\log n)^{c - o(1)}$ .

FormalConjectures/ErdosProblems/942.leanErdos942.erdos_9426 linesExact file

1True ↔2  ∃ c > 0,3    ∃ o,4      o =o[Filter.atTop] 1 ∧5        (∀ᶠ (n : ℕ) in Filter.atTop, ↑(Erdos942.erdos_942.h n) < Real.log ↑n ^ (c + o n)) ∧6          {n | ↑(Erdos942.erdos_942.h n) > Real.log ↑n ^ (c - o n)}.Infinite

OpenStatement only, no proof

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