Data obtained by the associated production of A hypernuclei through the (n + ,K + ) reaction are presented for a wide range of mass numbers. The special features which make this reaction useful are pointed out. The reaction is shown to be an excellent probe of A single-particle states, as demonstrated by the excitation of deeply bound states which are interpreted as the weak coupling of a A to neutronhole states of the core. The A binding energies and ground-state production cross sections for JvBe, 'AC, '&>, 2 2Si, ^Ca, 5 A V, and ^Y are presented.