A Further Combinatorial Number Theoretic Extension of Euler′s Totient
Received:December 11, 1995  
Key Words: Euler′s totient   regular convolution   restricted sets of integers (mod n)  
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Author NameAffiliation
Pentti Haukkanen Dept. of Math. Scis.
University of Tampere
P.O.Box 607
FIN-33101Tampere
Finland 
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Abstract:
      Recently, L.C.Hsu and Wang Jun generated new combinatorial number theoreticfunctions serving as generalizations of Euler′s totient. In this paper we form an extensive class of generalized Euler totients by translating the most general counting functions of Hsu and Wang on integers to the setting of Narkiewicz′s regular convolution. This class casts in the same framework various famous generalizations of Euler′s totient, such as Cohen′s totient, Jordan′s totient, Klee′s totient, Schemmel′s totient,Stevens′s to tient, the unitary analogue of Euler′s to tient and Euler′s to tient with respect to Narkiew icz′s regular convo lution.
Citation:
DOI:10.3770/j.issn:1000-341X.1997.04.008
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