Vol. 79, No. 2, 1978

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A convolution related to Golomb’s root function

E. E. Guerin

Vol. 79 (1978), No. 2, 463–467
Abstract

The root function γ(n) is defined by Golomb for n > 1 as the number of distinct representations n = ab with positive integers a and b. In this paper we define a convolution such that γ is the -analog of the (Dirichlet) divisor function τ. The structure of the ring of arithmetic functions under addition and is discussed. We compute and interpret -analogs of the Moebius function and Euler’s Φ-function. Formulas and an algorithm for computing the number of distinct representations of an integer n 2 in the form n = a1a2cdot ak , with ai a positive integer, i = 1,,k, are given.

Mathematical Subject Classification
Primary: 10A20, 10A20
Milestones
Received: 3 October 1977
Published: 1 December 1978
Authors
E. E. Guerin