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Arithmetic functions associated with infinitary divisors of an integer

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  • Graeme L. Cohen
  • Peter Hagis

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.

Suggested Citation

  • Graeme L. Cohen & Peter Hagis, 1993. "Arithmetic functions associated with infinitary divisors of an integer," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 16, pages 1-11, January.
    • Handle: RePEc:hin:jijmms:842035
    DOI: 10.1155/S0161171293000456
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    Cited by:

    1. Joseph Vade Burnett & Sam Grayson & Zachary Sullivan & Richard Van Natta & Luke Bang, 2018. "Arithmetical Functions Associated with the -ary Divisors of an Integer," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2018, pages 1-7, June.

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