The permutation of integers with small least common multiple of two subsequent terms

摘要

Erdős, Freud and Hegyvári [1] constructed a permutation a ₁,a ₂,… of positive integers with [a_i, a_i+1] 0 there exists an i ₀ with [a_i, a_i+1]allowbreak < iexp{(2Ö2+e) Ö{logiloglogi} }[a_{i}, a_{i+1}]allowbreak < iexp left{left(2sqrt{2}+varepsilonright) sqrt{log iloglog i},right} for all i≧i ₀.