Compositions of n Satisfying Some Coprimality Conditions
  A k-composition of n is a sequence of length k of positive integers summing up to n. In this paper, we investigate the number of k-compositions of n satisfying two natural coprimality conditions. Namely, we first give an exact asymptotic formula for the number of k-compositions having the first summand coprime to the others. Then, we estimate the number of k-compositions whose summands are all pairwise coprime. 
Daniela Bubboloni, Florian Luca, Pablo Spiga
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