Some properties of the pseudo-Smarandache function

Details Some properties of the pseudo-Smarandache function Some properties of the pseudo-Smarandache function

2005-04-06

arxiv.org/abs/math/0504118v1

Mathematics

Number Theory

Scientific paper

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

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