International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 2, Pages 373-383
doi:10.1155/S0161171293000456

Arithmetic functions associated with the infinitary divisors of an integer

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.