Charles Ashbacher [1] has posed a number of questions relating to the pseudo-Smarandache function Z(n). In this note we show that the ratio of consecutive values Z(n + 1)/Z(n) and Z(n - 1)/Z(n) are unbounded; that Z(2n)/Z(n) is unbounded; that n/Z(n) takes every integer value infinitely often; and that the series Σ_n 1/Z(n)^α is convergent for any α > 1.