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Claim. K. Lebensold, A divisibility problem, Studies in Appl. Math. 56 (1977), no. 3, 291--294, proves that $0.6725n\le f(n)\le0.6736n$ for all sufficiently large $n$, by decomposing $\{1,\ldots,n\}$ into divisibility chains, as the zbMATH review (Zbl 0367.10011) reports. The site and Guy's B24 state the same bound.

Covers. A two-sided bound on the first question of Problem 1062, how large $f(n)$ can be; not the existence of $\lim f(n)/n$ nor its irrationality. The formal-conjectures statement file states it as the solved variant erdos_1062.variants.lebensold_bounds.

Acceptance. A refereed journal publication (refereed). The site labels the problem OPEN, so its commentary is not acceptance. The issue is dated June 1977 and gives no day, so this page is named by the first day of that month.

Depends on. No page of this wiki.