Agentic AI-integrated robots are essential for effective, efficient, and safe Human-Robot collaboration (HRC), where robots must accurately interpret human behavior by understanding the working context. However, current human motion prediction models often focus on task-related context and rarely consider the robot as an influencing factor in HRC. This study navigates different contexts in human motion prediction for Agentic AI-empowered HRC, and proposes a robot-aware deep learning framework that integrates robot and task context into prediction. This framework handles context and human motions separately within a long short-term memory (LSTM)-based two-branch model to predict human motions in HRC tasks. The influence of different contextual information (e.g., robot actions, task-related object location) on prediction performance is also examined. The framework was implemented in a handover task and the results show that the proposed model improved performance by 7.95% in Average Displacement Error (ADE) and 8.74% in Final Displacement Error (FDE), compared to the baseline (i.e., without context). The findings indicate that context integration is critical for anticipating human motions, and the robot is an important context in HRC. This study advances the understanding of context integration in human motion prediction and contributes to the comprehension of AI-integrated robots in real-world HRC.