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The constant factor in the asymptotic for practical numbers

Number Theory 2019-08-30 v3

Abstract

An integer n1n\ge 1 is said to be practical if every natural number mn m \le n can be expressed as a sum of distinct positive divisors of nn. The number of practical numbers up to xx is asymptotic to cx/logxc x/\log x, where cc is a constant. In this note we show that c=1.33607...c=1.33607....

Keywords

Cite

@article{arxiv.1906.07819,
  title  = {The constant factor in the asymptotic for practical numbers},
  author = {Andreas Weingartner},
  journal= {arXiv preprint arXiv:1906.07819},
  year   = {2019}
}

Comments

10 pages

R2 v1 2026-06-23T09:57:24.905Z