A natural number n is said to be a (k, r)-integer if n = a^kb, where k > r > 1 and b is not divisible by the rth power of any prime. We study the distribution of such (k, r)-integers in the Piatetski-Shapiro sequence {⌊n^c⌋} with c > 1. As a corollary, we also obtain similar results for semi-r-free integers.

中文翻译：

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关于Piatetski-Shapiro序列中（k，r）整数的分布

如果n = a ^k b，则自然数n被称为（k，r）^整数，其中k> r > 1且b无法被任何质数的r次幂整除。我们研究这些（分布K，R）-integers在Piatetski-夏皮罗序列{⌊ Ñ ^Ç ⌋}与Ç > 1.作为推论，我们也获得了类似的半结果ř -free整数。