For each positive integer r, let Sr denote the rth Schemmel totient function, a multiplicative arithmetic function defined by Sr(p?) = ( 0, if p ? r; p?1(p r), if p > r for all primes p and positive integers ?. The function S1 is simply Euler’s totient function . Masser and Shiu have established several fascinating results concerning sparsely totient numbers, positive integers n satisfying (n) < (m) for all integers m > n. We define a sparsely Schemmel totient number of order r to be a positive integer n such that Sr(n) > 0 and Sr(n) < Sr(m) for all m > n with Sr(m) > 0. We then generalize some of the results of Masser and Shiu.
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