Vol. 62, No. 1, 1976

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ISSN: 0030-8730
Composite numbers and prime regressive isols

Joseph Barback

Vol. 62 (1976), No. 1, 49–53
Abstract

Let w(x), be the principal function for the set of all composite nonnegative integers and let Dw denote its canonical extension to the isols. M. Hassett proved in Comp. M. 26 (1973), as an application of a very general theorem, that if A is any T-regressive isol then Dw(A) is a regressive isol that is prime. The present paper contains a number theoretic proof of the following property: if Y is any infinite multiple-free regressive isol then Dw(Y ) is a regressive isol that is prime.

Mathematical Subject Classification
Primary: 02F40, 02F40
Milestones
Received: 23 June 1975
Revised: 14 October 1975
Published: 1 January 1976
Authors
Joseph Barback