@MISC{MOEBIUS2.MIZ,
  AUTHOR = {Grabowski, Adam},
  TITLE = {On Square-free Numbers},
  SECTION1 = {Preliminaries},
  SECTION2 = {Prime Numbers},
  SECTION3 = {Prime Reciprocals},
  SECTION4 = {Square Factors},
  SECTION5 = {Extracting Square-Containing and Square-Free Part of a Number},
  SECTION6 = {Binary Operations},
  SECTION7 = {On the Natural Divisors},
  SECTION8 = {The Lattice of Natural Divisors},
  DAY = {12},
  MONTH = {July},
  YEAR = {2013},
  ADDRESS1 = {Institute of Informatics\\University of Bia{\l}ystok\\Akademicka 2, 15-267 Bia{\l}ystok\\Poland},
  SUMMARY = {In the article the formal characterization of
  square-free numbers is shown; in this manner the paper is the continuation
  of \cite{MOEBIUS1.ABS}.
  Essentially, we prepared some lemmas for convenient work with numbers
  (including the proof that the sequence of prime reciprocals
  diverges \cite{PFTB}) according to \cite{HardyWright}
  which were absent in the Mizar Mathematical Library.
  Some of them were
  expressed in terms of clusters' registrations, enabling automatization
  machinery available in the Mizar system.
  Our main result of the article is in the final section;
  we proved that the lattice of positive divisors
  of a positive integer $n$ is Boolean if and only if
  $n$ is square-free.}}

