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The Number of Unitarily k-Free Divisors of An Integer

Published online by Cambridge University Press:  09 April 2009

D. Suryanarayana  and
R. Sita Rama Chandra Rao
D. Suryanarayana
Affiliation:
Department of Mathematics, Andhra University Waltair, India.
R. Sita Rama Chandra Rao
Affiliation:
Department of Mathematics, Andhra University Waltair, India.
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Let k be a fixed integer ≧ 2. A positive integer n is called unitarily k-free, if the multiplicity of each prime factor of n is not a multiple of k; or equivalently, if n is not divisible unitarily by the k-th power of any integer > 1. By a unitary divisor, we mean as usual, a divisor d> 0 of n such that (d, n/d) = 1. The interger 1 is also considered to be unitarily k-free. The concept of a unitarily k-free integer was first introduced by Cohen (1961; §1). Let denote the set of unitarily k-free integers. When k = 2, the set coincides with the set Q* of exponentially odd integers (that is, integers in whose canonical representation each exponent is odd) discussed by Cohen himself in an earlier paper (1960; §1 and §6). A divisor d > 0 of the positive integer n is called a unitarily k-free divisor of n if d ∈ . Let (n) denote the number of unitarily k-free divisors of n.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 1 , February 1976 , pp. 19 - 35
Copyright
Copyright © Australian Mathematical Society 1976

References

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