Some properties of the pseudo-Smarandache function

2005/04/06 by Richard G. E. Pinch, R. G. E. Pinch, Pinch, R. G. E.
Mathematics · #11A25 #11B83 #Advanced Mathematical Theories #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11A25 #msc:11B83

paper · pdf · doi:10.48550/arxiv.math/0504118

arxiv created 2005/04/06 · openalex publication_date 2005/04/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We answer a number of questions relating to the pseudo-Smarandache function Z(n). 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 ∑_n 1/Z(n)^α is convergent for any α> 1.

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