A sum of a certain divisor function for arithmetical semi-groups

E. M. Horadam

Vol. 22 (1967), No. 3, 407–412

DOI: 10.2140/pjm.1967.22.407

Abstract

Let {b_n} 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 b_n = dδ and let τ′(b_n) denote the number of divisors d of b_n where both d are δ and square free. Then it is shown here that T(x) defined by

where A is a constant depending on b_u.

Mathematical Subject Classification

Primary: 10.43

Milestones

Received: 29 April 1965

Published: 1 September 1967