The infinitary divisors of a natural number n are the products of its divisors of the form p y α 2 α , where p y is a prime-power component of n and ∑ α y α 2 α (where y α = 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.