Let [Formula: see text] be an arbitrary real-valued positive nondecreasing function, in this paper we prove that [Formula: see text] [Formula: see text] where [Formula: see text] is the sum given in the title, [Formula: see text] and [Formula: see text] is a positive integer. This improves the result of Mercier and Nowak.

中文翻译：

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关于和∑n≤xf(n){x/n}k的渐近行为

令[Formula: see text]为任意实值正非减函数，本文证明[Formula: see text] [Formula: see text] 其中[Formula: see text]是标题中给出的和， [公式：见正文]和[公式：见正文]为正整数。这改善了 Mercier 和 Nowak 的结果。