On a sum involving the Euler funtion
On a sum involving the Euler funtion
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关于涉及欧拉函数的和
DOI：
10.1016/j.jnt.2019.01.006
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Igro E. Shparlinski
中科院分区：
文献类型：
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作者：
Oliver Bordelles;Li-Xia Dai;R;ell Heyman;Hao Pan;Igro E. Shparlinski
We obtain reasonably tight upper and lower bounds on the sum∑ n⩽ x φ (⌊ x/n⌋), involving the Euler functions φ and the integer parts⌊ x/n⌋ of the reciprocals of integers. For slower growing arithmetic functions f we obtain asymptotic formulas for similar sums of f (⌊ x/n⌋). These are analogues of a series of previous results for sequences involving the integer part functions such Beatty and Piatetski–Shapiro sequences.
