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Recently, researchers have shown an increased interest in the area of energy efficient operation of the sensors inside the wireless sensor networks (WSNs). The energy efficiency could be achieved by designing an effective routing protocol. Cluster based routing protocol is a well known technique to increase the energy efficiency of the sensor nodes as well as extending the lifetime of the network. Cluster based routing protocol was formed a number of clusters which gather the data sensed from all sensor nodes in the network. Then, the data were sent to the sink node. In addition, the number of clusters needs to be selected properly to avoid faster network degradation. This paper shows the derivation of an analytical formula to optimize the number of clusters (k) in three level heterogeneous wireless sensor networks in order to increase the network lifetime. It was formulated by considering the energy consumption per iteration. Simulation results verify both the correctness of our mathematical models and the effectiveness of computing the k value to increase the network lifetime.