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@PeterTaylor, also, about your draft edit to A248667: maybe A000522(n-1) instead of A000522(n+1)? There also exists A248666, where you can put the same comment.
@PeterTaylor, thank you for answer! Can you compute another counterexamples? At least 2 more to add the sequence to the OEIS. By the way, the numbers might be called your last name.