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Ambient energy harvesting can help to mitigate the typical finite energy supply of sensor nodes in wireless sensor networks (WSNs). Energy harvesting WSNs (EH-WSNs) offer new challenges in terms of network protocol design and resource management (such as task allocation, data collection, etc. ) that do not exist in conventional battery powered systems. In this work, the novel task allocation for EH-WSNs with solar powered sensor nodes is proposed which operates in two phases of task scheduling and task mapping to the sensor nodes. Initial simulations show promising results in terms of energy balancing (maximizing) among the nodes and scheduling length (minimizing), in the presence of energy harvesting.