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Claim. Let $\tau^+(n)$ count the $k$ with a divisor of $n$ in $[2^k,2^{k+1})$. Hall and Tenenbaum, Divisors, Cambridge Tracts in Mathematics 90, Cambridge University Press, 1988, Chapter 4 (the site cites Section 4.6), prove that $\tau^+(n)/\tau(n)$ has a limiting distribution function $\nu$ satisfying

$$\frac{z}{\sqrt{\log(2/z)}}\ll\nu(z)\ll z\log(2/z)\qquad(0<z<1).$$

The statement is taken from Tenenbaum's survey of 2013, equation (15) on p. 7 of the author's version (Tenenbaum 2013), which reports the theorem as an improvement of the Erdős–Tenenbaum estimate that had already refuted the conjecture. The density of $\{n:\tau^+(n)<\epsilon\tau(n)\}$ is at most $\nu(\epsilon)$, which is below one for small $\epsilon$, so the set does not have density one and the answer to Problem 448 is no. The upper bound sharpens the Erdős–Tenenbaum bound $c(\varepsilon)\alpha^{1-\varepsilon}$ on the upper density of $\{n:\tau^+(n)\le\alpha\tau(n)\}$, recorded on their claim page; the site's commentary records the sharper bound as $\ll\epsilon\log(2/\epsilon)$ and the existence of the distribution function. The formal-conjectures file FormalConjectures/ErdosProblems/448.lean, at its commit of 2026-09-18, states the bound and the distribution function as the variants hall_tenenbaum_upper_bound and hall_tenenbaum_distribution, both without proof.

Acceptance. The book is a monograph, not a journal publication, so no refereed evidence is listed. The site credits the sharper bound and the distribution function to Hall and Tenenbaum but the disproof of the problem to Erdős and Tenenbaum, so no reviewed evidence is listed either; Tenenbaum's survey is by a co-author and is not independent acceptance. The problem's standing derives from the accepted Erdős–Tenenbaum page. This repository has not checked the proof.