## Some Properties of the Pseudo-Smarandache Function

**Authors:** Richard Pinch

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.

**Comments:** 6 pages

**Download:** **PDF**

### Submission history

[v1] 22 Aug 2010

**Unique-IP document downloads:** 30 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*