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 statement2 of 3

It is not hard to prove that the density $\delta_l$ of integers for which $h(n) = l$ exists and satisfies $\sum_l \delta_l = 1$ .

FormalConjectures/ErdosProblems/942.leanErdos942.erdos_942.variants.density1 lineExact file

1∃ δ, ∀ (l : ℕ), {n | Erdos942.erdos_942.h n = l}.HasDensity (δ l) ∧ ∑' (l : ℕ), δ l = 1

TextbookStatement only, no proof