2020/07/12 by Bubboloni, Daniela, Luca, Florian
#05A17 #11A25 #11N37 #11P81 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2007.05972
We show that while the number of coprime compositions of a positive integer n into k parts can be expressed as a ℚ-linear combinations of the Jordan totient functions, this is never possible for the coprime partitions of n into k parts. We also show that the number pk'(n) of coprime partitions of n into k parts can be expressed as a ℂ-linear combinations of the Jordan totient functions, for n sufficiently large, if and only if k∈ \2,3\ and in a unique way. Finally we introduce some generalizations of the Jordan totient functions and we show that pk'(n) can be always expressed as a ℂ-linear combinations of them.