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Generating Functions for a Class of Arithmetic Functions

Published online by Cambridge University Press:  20 November 2018

A. A. Gioia  and
M.V. Subbarao
A. A. Gioia
Affiliation:
Texas Technological College and University of Alberta
M.V. Subbarao
Affiliation:
Texas Technological College and University of Alberta
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In this note the arithmetic functions L(n) and w(n) denote respectively the number and product of the distinct prime divisors of the integer n ≥ 1, and L(l) = 0, w(l) = 1. An arithmetic function f is called multiplicative if f(1) = 1 and f(mn) = f(m)f(n) whenever (m, n) = 1. It is known ([1], [3], [4]) that every multiplicative function f satisfies the identity

1.1

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 9 , Issue 4 , October 1966 , pp. 427 - 431
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Gioia, A. A., On an identity for multiplicative functions, Amer. Math. Monthly 69, (1962), pages 988-991.Google Scholar
2. Subbarao, M.V., A generating function for a class of arithmetic functions. Amer. Math. Monthly 70, (1963), pages 841-842.Google Scholar
3. Vaidyanathaswamy, R., The identical equations of the multiplicative function. Bull. Amer. Math. Soc. 36, (1930), pages 762-772.Google Scholar
4. Vaidyanathaswamy, R., The theory of multiplicative arithmetic functions. Trans. Amer. Math. Soc. 33, (1931), pages 579-662.Google Scholar