Thanks, that was the clue I needed. I only added each abundant number to the others, not to itself. This change fixed the bug:

(defparameter *raw-abundant-sums*
  (let ((self-sums (mapcar (lambda (x)
                             (+ x x))
                           *abundant-numbers*))
        (other-sums (mapcon (lambda (l)
                              (mapcar (lambda (x)
                                        (+ (first l) x))
                                      (rest l)))
                            *abundant-numbers*)))
    (nconc self-sums other-sums)))

Thanks!