A Class of Rational Arithmetical Functions with Combinatorial Meanings
Received:December 11, 1995  
Key Words: Euler totient function   regular convolutions   multiplicative functions  
Fund Project:
Author NameAffiliation
Pentti Haukkanen Dept. of Math. Scis.
Univ. of Tampere
P.O.Box 607
FIN 33101 Tampere
Finland 
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Abstract:
      An arithmetical function f is said to be a rational arithmetical function of order (s,r) if there existcompletely multiplicative functions f1,f2,…,fs and g1,g2,…,gr such thatf=f1*f2*… *fs*(g1)-1*(g2)-1*… *(gr) -1 ,where * is the Dirichlet convolution. Recently, L.C. Hsu and Wang Jun studied combinatorial meanings of rational arithmetical functions of order (1,r) . We study these meanings in the setting of Narkiewicz's regular convolution.
Citation:
DOI:10.3770/j.issn:1000-341X.1997.02.005
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