aliquot-seq

;; BY CLAUDE:

;; Aliquot-Sequenz (Summe echter Teiler, Zyklus = befreundete Zahlen)
(defun aliquot-seq (n &optional acc)
  "Sequenz n → Σ(echte Teiler) bis 0, Fixpunkt oder Zyklus."
  (let ((acc (or acc (list n))))
    (let ((next (reduce #'+ (proper-divisors n) :initial-value 0)))
      (cond
        ((zerop next)        (append acc (list 0)))        ; endet bei 0
        ((member next acc)   (append acc (list next)))     ; Zyklus
        (t (aliquot-seq next (append acc (list next))))))))


(list-plot  (aliquot-seq (random 100))  :join-points t)
(list-plot (loop repeat 10
                   collect (aliquot-seq (random 100)))
           :join-points t)