Explicit bounds for Buchstab's function

Andreas Weingartner

Explicit bounds for Buchstab's function

Number Theory 2026-07-24 v1

Authors: Andreas Weingartner

Abstract

Buchstab's function $\omega(u)$ describes the distribution of integers without small prime factors. We establish numerically explicit upper and lower bounds for $\omega(u)$ that are easy to evaluate, without the need to solve the delay differential equation numerically.

Cite

@article{arxiv.2607.21883,
  title  = {Explicit bounds for Buchstab's function},
  author = {Andreas Weingartner},
  journal= {arXiv preprint arXiv:2607.21883},
  year   = {2026}
}

Comments

15 pages, 1 figure