Some properties of the pseudo-Smarandache function

R. G. E. Pinch

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Some properties of the pseudo-Smarandache function

R. G. E. Pinch

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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 $\sum_n 1/Z(n)^α$ is convergent for any $α> 1$.

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R. G. E. Pinch. 2005-04-06. Some properties of the pseudo-Smarandache function. https://arxiv.org/abs/math/0504118

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