Some properties of the pseudo-Smarandache function

R. G. E. Pinch

Some properties of the pseudo-Smarandache function

数论 2007-05-23 v1

作者: R. G. E. Pinch

摘要

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 $\alpha > 1$ .

关键词

multiplicative functions zeta values and euler sums collatz conjecture

引用

@article{arxiv.math/0504118,
  title  = {Some properties of the pseudo-Smarandache function},
  author = {R. G. E. Pinch},
  journal= {arXiv preprint arXiv:math/0504118},
  year   = {2007}
}

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