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On arithmetic functions and divisors of higher order

Published online by Cambridge University Press:  09 April 2009

Krishnaswami Alladi
Krishnaswami Alladi
Affiliation:
Department of Mathematics, Vivekananda College, Madras, India.
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Abstract

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We discuss properties of arithmetic functions of higher order defined through the introduction of a new concept of divisor of higher order. We shall construct an infinite sequence of Euler-like functions and the well known Euler function will be the first member of this sequence. Asymptotic estimates of such functions are given and a study of error functions associated with the Euler-like sequence is made. We would like to mention that the familiar number theoretic functions become only the first members of an infinite sequence of functions of similar behaviour.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 1 , February 1977 , pp. 9 - 27
Copyright
Copyright © Australian Mathematical Society 1977

References

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