This paper considers cognitive radio networks (CRNs) utilizing multiple time-slotted primary channels in which cognitive users (CUs) are powered by energy harvesters. The CUs are under the consideration that hardware constraints on radio devices only allow them to sense and transmit on one channel at a time. For a scenario where the arrival of harvested energy packets and the battery capacity are finite, we propose a scheme to optimize (i) the channel-sensing schedule (consisting of finding the optimal action (silent or active) and sensing order of channels) and (ii) the optimal transmission energy set corresponding to the channels in the sensing order for the operation of the CU in order to maximize the expected throughput of the CRN over multiple time slots. Frequency-switching delay, energy-switching cost, correlation in spectrum occupancy across time and frequency and errors in spectrum sensing are also considered in this work. The performance of the proposed scheme is evaluated via simulation. The simulation results show that the throughput of the proposed scheme is greatly improved, in comparison to related schemes in the literature. The collision ratio on the primary channels is also investigated.