Composite numbers and prime regressive isols

Abstract

Let w(jc),be the principal function for the set of all composite nonnegative integers and let D w 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 D W () 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 D W (Y) is a regressive isol that is prime.