Counting carefree couples
arXiv:math/0510003
Abstract
A pair of natural numbers (a,b) such that a is both squarefree and coprime to b is called a carefree couple. A result conjectured by Manfred Schroeder (in his book `Number theory in science and communication') on carefree couples and a variant of it are established using standard arguments from elementary analytic number theory. Also a related conjecture of Schroeder on triples of integers that are pairwise coprime is proved.
Updated version of 2005 update of 2000 version. Improved and expanded presentation. In estimate (2) now only a weaker error term than before is obtained