The harmonic flow coefficients vn with n=2,3,4 are measured for neutral pions and inclusive charged hadrons in Au-Au collisions at sqrt(s_NN) = 62 and 39 GeV with the PHENIX detector at the Relativistic Heavy Ion Collider (RHIC). These vn coefficients characterize the anisotropy of particle productions in the azimuth at different angular scale, which are sensitive to the transport properties and initial spatial asymmetries of the hot and dense medium created in these collisions. Significant values of vn are observed for neutral pions (for n = 2) and inclusive charge hadron (for n = 2, 3, 4) at both collision energies, spanning broad ranges of transverse momentum pT and collision centrality. These results are compared to measurements at other beam energies from RHIC, and to the recent results at sqrt(s_NN) = 2760 GeV from the Large Hadron Collider (LHC). The magnitudes of the vn are found to be similar over the range of sqrt(s_NN) =39-2760 GeV. However, the v2 values for inclusive charge hadron are found to decrease significantly for collisions at sqrt(s_NN) < 39 GeV, and essentially reaches 0 at sqrt(s_NN) around 3 GeV. These results provide important input for studying the transport properties and the initial geometry profiles of the hot and dense matter created in Au+Au collisions at sqrt(s_NN) = 62 and 39 GeV. They also serve as important components in the beam energy scan of vn, which might help locate the critical point of the QCD phase diagram.