Extensive new results for the natural radiative lifetimes of the perturbed odd-parity 6snf 3F3, 1F3, and 3F4 sequences of barium (with 11 < n < 40, 11 < n < 40 and 13 < n < 40, respectively) have been calculated. The calculations were performed in the framework of multichannel quantum defect theory. The contributions to the transition probabilities of all known even-parity levels of the 6snd and 6sng configurations together with their perturber states and connected via the electric dipole operator with the 6snf 3F, 1F3, and 3F4 levels, are considered.The results for the 6snf 1F3 and 3F4 sequences, in contrast with those for the 6snf 3F3 series, show strong deviation from a hydrogenic scaling law. This deviation reflects the extended perturbations of these levels by some of the doubly excited states of the same parity.