Neural networks often make overconfident predictions from out-of-distribution (OOD) samples. Detection of OOD data is therefore crucial to improve the safety of machine learning. The simplest and most powerful method for OOD detection is MaxLogit, which uses the model's maximum logit to provide an OOD score. We have discovered that, in addition to the maximum logit, some other logits are also useful for OOD detection. Based on this finding, we propose a new method called ATLI (Adaptive Top-k Logits Integration), which adaptively determines effective top-k logits that are specific to each model and combines the maximum logit with the other top-k logits. In this study we evaluate our proposed method using ImageNet-1K benchmark. Extensive experiments showed our proposed method to reduce the false positive rate (FPR95) by 6.73% compared to the MaxLogit approach, and decreased FPR95 by an additional 2.67% compared to other state-of-the-art methods.