In this note, we study the representation of a natural number as the sum of three natural numbers having the form âŒŠn2 a âŒ‹ (n âˆˆ N), where a is a fixed positive integer and âŒŠ.âŒ‹ denotes the integer-partâ€¦ (More)

When studying the least common multiple of some nite sequences of integers, the rst author introduced the interesting arithmetic functions gk (k âˆˆ N), de ned by gk(n) := n(n+1)...(n+k)â€¦ (More)

In this paper, we prove the following result: Let A be an infinite set of positive integers. For all positive integer n, let Ï„n denote the smallest element of A which doesnâ€™t divide n. Then we haveâ€¦ (More)

The purpose of this paper is to study the arithmetic function f : Z+ â†’ Q âˆ— + defined by f(2l) = l (âˆ€k, l âˆˆ N, l odd). We have, for example, f(1) = 1, f(2) = 1, f(3) = 3, f(12) = 1 3 , f(40) = 1 25 ,â€¦ (More)