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- W107528871 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.
- W107528871 created "2016-06-24" @default.
- W107528871 creator A5050123780 @default.
- W107528871 date "2014-12-09" @default.
- W107528871 modified "2023-09-27" @default.
- W107528871 title "On Schemmel Nontotient Numbers" @default.
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- W107528871 hasPublicationYear "2014" @default.
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