Corpus ID: 155099883

# Cardinality of a Floor Function Set

@article{Heyman2019CardinalityOA,
title={Cardinality of a Floor Function Set},
author={Randell Heyman},
journal={Integers},
year={2019},
volume={19},
pages={A67}
}
Fix a positive integer X. We quantify the cardinality of the set $\{\lfloor X/n \rfloor\}_{n=1}^X$. We discuss restricting the set to those elements that are prime, semiprime or similar.

#### References

SHOWING 1-4 OF 4 REFERENCES
On a sum involving the Euler function
• Mathematics
• Journal of Number Theory
• 2019
We obtain reasonably tight upper and lower bounds on the sum $\sum_{n \leqslant x} \varphi \left( \left\lfloor{x/n}\right\rfloor\right)$, involving the Euler functions $\varphi$ and the integer partsExpand
On a partial sum related to the Euler totient function.
Recently, Bordell\'{e}s, Dai, Heyman, Pan and Shparlinski in \cite{Igor} considered a partial sum involving the Euler totient function and the integer parts $\lfloor x/n\rfloor$ function. Among otherExpand
Mean square of zeta function, circle problem and divisor problem revisited
• Mathematics
• 2017
This paper is closely related to the recent work [BW17] of the same authors and our purpose is to elaborate more on some of the results and methods from [BW17]. More specifically our goal isExpand
NOTE ON SUMS INVOLVING THE EULER FUNCTION
• Shane Chern
• Mathematics
• Bulletin of the Australian Mathematical Society
• 2019
In this note, we provide refined estimates of two sums involving the Euler totient function, \begin{eqnarray}\mathop{\sum }_{n\leqExpand