Counting carefree couples

Pieter Moree

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Counting carefree couples

Pieter Moree

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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.

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Pieter Moree. 2014-07-04. Counting carefree couples. https://arxiv.org/abs/math/0510003

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