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On f(n) modulo Ω(n) and ω(n) when f is a polynomial

Part of: Multiplicative number theory Elementary number theory

Published online by Cambridge University Press:  09 April 2009

Florian Luca
Florian Luca
Affiliation:
Mathematical Institute, UNAM, Ap. Postal 61-3 (Xangari), CP 58 089 Morelia, Michoacán, Mexico e-mail: fluca@matmor.unam.mx
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Abstract

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In this paper we show that if f (X) ∈; Z [X ] is a nonzero polynomial, then ω(n)/f(n) holds only on a set of n of asymptotic density zero, where for a positive integer n the number ω(n) counts the number of distinct prime factors ofn.

Keywords

sum-of-divisors functionEuler functionnumber of prime divisors function

MSC classification

Secondary: 11A25: Arithmetic functions; related numbers; inversion formulas 11N37: Asymptotic results on arithmetic functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 77 , Issue 2 , October 2004 , pp. 149 - 164
Copyright
Copyright © Australian Mathematical Society 2004

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