Number Theory


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 Σn 1/Z(n)α is convergent for any α > 1.

Comments: 6 pages

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[v1] 22 Aug 2010

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