We consider a Sensor-Aided Cognitive Radio Network (SACRN) in which sensors capable of harvesting energy are distributed throughout the network to support secondary transmitters for sensing licensed channels in order to improve both energy and spectral efficiency. Harvesting ambient energy is one of the most promising solutions to mitigate energy deficiency, prolong device lifetime, and partly reduce the battery size of devices. So far, many works related to SACRN have considered single secondary users capable of harvesting energy in whole slot as well as short-term throughput. In the paper, we consider two types of energy harvesting sensor nodes (EHSN): Type-I sensor nodes will harvest ambient energy in whole slot duration, whereas type-II sensor nodes will only harvest energy after carrying out spectrum sensing. In the paper, we also investigate long-term throughput in the scheduling window, and formulate the throughput maximization problem by considering energy-neutral operation conditions of type-I and -II sensors and the target detection probability. Through simulations, it is shown that the sensing energy consumption of all sensor nodes can be efficiently managed with the proposed scheme to achieve optimal long-term throughput in the window.