Abstract
We show that while the number of coprime compositions of a positive integer n into k parts can be expressed as a Q-linear combination 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 combination 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 combination of them.
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