Asymptotics of Landau--Okhotin function

TL;DR

This paper derives precise logarithmic asymptotics for a specialized Landau function variant, $ ilde{g}(n)$, which maximizes the least common multiple of integers with specific progression constraints.

Contribution

It provides the first sharp asymptotic formula for $ ilde{g}(n)$ under the given conditions, advancing understanding of LCM behavior in structured integer sets.

Findings

Sharp logarithmic asymptotics for $ ilde{g}(n)$

Asymptotic behavior characterized precisely

Improves understanding of LCM in arithmetic progressions

Abstract

Landau function $g(n)$ is the maximal possible least common multiple of several positive integers with sum not exceeding $n$. Under additional assumptions that these numbers are the differences of disjoint bi-infinite arithmetic progressions the maximum is denoted $\tilde{g}(n)$, it was introduced by Okhotin. We find a sharp logarithmic asymptotics of $\tilde{g}(n)$.