Type: Article

Compositions of n satisfying some coprimality conditions

Bubboloni, Daniela; Luca, Florian; Spiga, Pablo;

Abstract:

An l-composition of n is a sequence of length l of positive integers summing up to n. In this paper, we investigate the number of l-compositions of n satisfying two natural coprimality conditions. Namely, we first give an exact asymptotic formula for the number of l-compositions having the first summand coprime to the others. Then, we estimate the number of l-compositions whose summands are all pairwise coprime.