An experimental function for counting odd non-prime numbers

This work presents an experimental and computational study of a function that counts odd non-prime numbers up to a given bound. The approach is exploratory in nature and does not claim a complete theoretical proof.The author is seeking verification and feedback from the mathematical community.At this stage, I have a draft of the proof and several supporting arguments, but a complete and fully formal written proof will be presented in a future release. I am, of course, available to explain the reasoning in detail if requested.