Abstract
Erdős, Freud and Hegyvári [1] constructed a permutation a 1,a 2,… of positive integers with \([a_{i}, a_{i+1}]< i\exp \left\{c\sqrt{\log i}\log\log i\,\right\}\) for an absolute constant c>0 and all i≧3. In this note, we construct a permutation of all positive integers such that for any ε>0 there exists an i 0 with \([a_{i}, a_{i+1}]\allowbreak < i\exp \left\{\left(2\sqrt{2}+\varepsilon\right) \sqrt{\log i\log\log i}\,\right\}\) for all i≧i 0.
Similar content being viewed by others
References
P. Erdős, R. Freud and N. Hegyvári, Arithmetical properties of permutations of integers, Acta Math. Hungar., 41 (1983), 169–176.
E. Saias, Applications of integers with dense divisors, Acta Arith., 83 (1998), 225–240.
Author information
Authors and Affiliations
Corresponding author
Additional information
Corresponding author.
Research supported by the National Natural Science Foundation of China, Grant Nos. 11071121 and 10771103.
Rights and permissions
About this article
Cite this article
Chen, YG., Ji, CS. The permutation of integers with small least common multiple of two subsequent terms. Acta Math Hung 132, 307–309 (2011). https://doi.org/10.1007/s10474-011-0099-x
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10474-011-0099-x