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- W4294189490 abstract "For each positive integer $r$, let $S_r$ denote the $r^{th}$ Schemmel totient function, a multiplicative arithmetic function defined by [S_r(p^{alpha})=begin{cases} 0, & mbox{if } pleq r; p^{alpha-1}(p-r), & mbox{if } p>r end{cases}] for all primes $p$ and positive integers $alpha$. The function $S_1$ is simply Euler's totient function $phi$. We define a Schemmel nontotient number of order $r$ to be a positive integer that is not in the range of the function $S_r$. In this paper, we modify several proofs due to Zhang in order to illustrate how many of the results currently known about nontotient numbers generalize to results concerning Schemmel nontotient numbers. We also invoke Zsigmondy's Theorem in order to generalize a result due to Mendelsohn." @default.
- W4294189490 created "2022-09-02" @default.
- W4294189490 creator A5050123780 @default.
- W4294189490 date "2014-12-09" @default.
- W4294189490 modified "2023-10-14" @default.
- W4294189490 title "On Schemmel Nontotient Numbers" @default.
- W4294189490 doi "https://doi.org/10.48550/arxiv.1412.3089" @default.
- W4294189490 hasPublicationYear "2014" @default.
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