Arithmetic functions associated with the infinitary divisors of an integer (Q1210468)

The infinitary divisors of a natural number \(n\) are products of its divisors of the form \(p^{y_\alpha 2^\alpha}\), where \(p^y\) is a prime-power component of \(n\) and \(\sum_\alpha y_\alpha 2^\alpha\) (where \(y_\alpha=0\) or 1) is the binary representation of \(y\) [cf. \textit{G. L. Cohen}, Math. Comput. 43, 395--411 (1990; Zbl 0689.10014)]. The authors define ``infinitary'' analogues of such familiar concepts as the greatest common divisor, the Dirichlet convolution, multiplicative functions, Euler's totient, divisor functions and the Möbius function, and exhibit their basic properties.