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A Proof of an Identity for Multiplicative Functions

Published online by Cambridge University Press:  20 November 2018

K. Krishna
K. Krishna*
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, Penn, 15260
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An arithmetic function f is said to be multiplicative if f(mn) = f(m)f(n), whenever (m, n) = 1 and f(1) = 1. The Dirichlet convolution of two arithmetic functions f and g, denoted by f • g, is defined by f • g(n) = Σd|nf(d)g(n/d). Let w(n) denote the product of the distinct prime factors of n, with w(l) = 1. R.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 22 , Issue 3 , 01 September 1979 , pp. 299 - 304
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Gioia, A. A., The K-product of Arithmetic Functions, Canad. J. Math. 17 (1965), 970-976.Google Scholar
2. Subba Rao, M. V. and Gioia, A. A., Identities for multiplicative functions, Canad. Math. Bull. 10 (1967), 65-73.Google Scholar
3. Vaidyanathaswamy, R., The identical equations of the multiplicative function, Bull. Amer. Math. Soc. 36 (1930), 762-772.Google Scholar