  The hope that copper doped lead apatite Pb$_9$Cu(PO$_4$)$_6$O is a
room-temperature superconductor has largely been dashed by global research
efforts. Nevertheless, according to the current state of knowledge, the
material has interesting magnetic properties, and research groups around the
world have prepared high quality samples. We use a fluctuation exchange
approximation (FLEX) approach to study the magnetic tendencies in
Pb$_9$Cu(PO$_4$)$_6$O. We find ferromagnetic fluctuations very close to the
filling of the stoichiometric compound which can be understood from Fermi
surface nesting at the M point. This is similar to the one-band triangular
lattice Hamiltonian at three-quarter filling. Interestingly, the special kz
dependence of the Pb$_9$Cu(PO$_4$)$_6$O band structure makes it very sensitive
to doping. Only slight charge doping switches between antiferromagnetic and
ferromagnetic fluctuations. If the material could become superconducting, it
might be easily switchable between singlet and triplet superconductivity.
