Searches are performed for both prompt-like and long-lived dark photons, $A^{prime}$, produced in proton-proton collisions at a center-of-mass energy of 13 TeV, using $A^{prime}tomu^+mu^-$ decays and a data sample corresponding to an integrated luminosity of 1.6 fb$^{-1}$ collected with the LHCb detector. The prompt-like $A^{prime}$ search covers the mass range from near the dimuon threshold up to 70 GeV, while the long-lived $A^{prime}$ search is restricted to the low-mass region $214<m(A^{prime})<350$ MeV. No evidence for a signal is found, and 90% confidence level exclusion limits are placed on the $gamma$-$A^{prime}$ kinetic-mixing strength. The constraints placed on prompt-like dark photons are the most stringent to date for the mass range $10.6 < m(A^{prime}) < 70$ GeV, and are comparable to the best existing limits for $m(A^{prime}) < 0.5$ GeV. The search for long-lived dark photons is the first to achieve sensitivity using a displaced-vertex signature.
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