## 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

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### Submission history

[v1] 22 Aug 2010

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