Large strings of consecutive smooth integers

Filip Najman

Large strings of consecutive smooth integers

Number Theory 2011-11-24 v1

Authors: Filip Najman

Abstract

In this note we improve an algorithm from a recent paper by Bauer and Bennett for computing a function of Erd\"os that measures the minimal gap size $f(k)$ in the sequence of integers at least one of whose prime factors exceeds $k$ . This allows us to compute values of $f(k)$ for larger $k$ and obtain new values of $f(k)$ .

Keywords

prime numbers combinatorial bounds and extremal problems divisor function

Cite

@article{arxiv.1108.3710,
  title  = {Large strings of consecutive smooth integers},
  author = {Filip Najman},
  journal= {arXiv preprint arXiv:1108.3710},
  year   = {2011}
}

Comments

7 pages, to appear in Arch. Math. (Basel)

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