Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  453.10004
Autor:  Erdös, Pál; Györy, Kalman; Papp, Zoltan
Title:  On some new properties of functions \sigma(n), \phi(n), d(n) and \nu(n). (In Hungarian)
Source:  Mat. Lapok 28, 125-131 (1980).
Review:  The authors call two functions f(n) and g(n) independent if, for any two permutations i1,... ir; j1... jr of 1,2,...,r, the inequalities f(n+i1) > ... > f(n+ir); f(n+j1) > ... > f(n+jr) have always infinitely many solutions. They prove that d(n) and \theta(n) are independent. For \phi(n) and \sigma(n) the result holds for r \leq 4 only.
If the definition is extended to the independence of k functions (with arbitrary k permutations) then d(n), \theta(n) and either \phi(n) or \sigma(n) are also independent.
Reviewer:  A.Recski
Classif.:  * 11A25 Arithmetic functions, etc.
Keywords:  independent functions; permutations

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