Abstract

The infinitary divisors of a natural number n are the products of its divisors of the form pyα2α, where py is a prime-power component of n and αyα2α (where yα=0 or 1) is the binary representation of y. In this paper, we investigate the infinitary analogues of such familiar number theoretic functions as the divisor sum function, Euler's phi function and the Möbius function.