journal6 ›› 2005, Vol. 26 ›› Issue (4): 76-78.

• Mathematics • Previous Articles     Next Articles

An  Arithmetic  Function  and the   K-th  Roots of  a  Postive Integers


  1. (College of Mathematics and Computer Science,Yan'an University,Yan'an 716000,Shannxi China)
  • Online:2005-10-15 Published:2012-09-17
  • About author:GAO Li(1966-),female,native of Suide,Shaanxi,professor of Yan'an University;field of research is analytic number theory.
  • Supported by:

    This  work  is  supported  by  the  Province  Education  Commission  Science  Foundation  of  Shaanxi(04JK301)

Abstract: Let  n  be  any  postive  integer,ak(n)  denotes  the  integer  part  of  k-th  root  of  n.Let  p  be  a  prime,ep(n)  denotes  the  largest exponent  of  power p which  divides  n.The  main  purpose  of  this  paper  is  to  study  the  mean  value  properties  of  ep(ak(n)) and  give  an  interesting  asymptotic  formula  for  it.

Key words: K-th root, largest exponent, asymptotic formula

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