Vol. 22, No. 3, 1967

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Vol. 286: 1  2
Vol. 285: 1  2
Vol. 284: 1  2
Vol. 283: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Subscriptions
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
A sum of a certain divisor function for arithmetical semi-groups

E. M. Horadam

Vol. 22 (1967), No. 3, 407–412
Abstract

Let {bn} denote the set of elements of a free ordered arithmetical semi-group with multiplication and a known counting function. Using the corresponding terminology of arithmetic let bn = and let τ(bn) denote the number of divisors d of bn where both d are δ and square free. Then it is shown here that T(x) defined by

        ∑
T(x) =       τ′(bn ) ∼ Ax logx
bn≦x
(bn,bu)=1

where A is a constant depending on bu.

Mathematical Subject Classification
Primary: 10.43
Milestones
Received: 29 April 1965
Published: 1 September 1967
Authors
E. M. Horadam