A 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.
Compositions of n satisfying some coprimality conditions / D. Bubboloni; F. Luca; P. Spiga. - In: JOURNAL OF NUMBER THEORY. - ISSN 0022-314X. - STAMPA. - 132 (12):(2012), pp. 2922-2946. [10.1016/j.jnt.2012.06.012]
Compositions of n satisfying some coprimality conditions
BUBBOLONI, DANIELA;
2012
Abstract
A 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.
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