Context: Annually, ICSE acknowledges a range of papers, a subset of which are paired with research artifacts such as source code, datasets, and supplementary materials, adhering to the Open Science Policy. However, no prior systematic inquiry dives into gauging the influence of ICSE papers using artifact attributes. Objective: We explore the mutual impact between artifacts and their associated papers presented at ICSE over ten years. Method: We collect data on usage attributes from papers and their artifacts, conduct a statistical assessment to identify differences, and analyze the top five papers in each attribute category. Results: There is a significant difference between paper citations and the usage of associated artifacts. While statistical analyses show no notable difference between paper citations and GitHub stars, variations exist in views and/or downloads of papers and artifacts. Conclusion: We provide a thorough overview of ICSE's accepted papers from the last decade, emphasizing the intricate relationship between research papers and their artifacts. To enhance the assessment of artifact influence in software research, we recommend considering key attributes that may be present in one platform but not in another.