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
© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag