Arithmetic functions associated with infinitary divisors of an integer

Graeme L. Cohen and Peter Hagis

International Journal of Mathematics and Mathematical Sciences, 1993, vol. 16, 1-11

Abstract:

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.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:842035

DOI: 10.1155/S0161171293000456

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