A007906 Number of steps for aliquot sequence for n to converge to 0, or -1 if it never reaches 0.

1, 2, 2, 3, 2, -1, 2, 3, 4, 4, 2, 7, 2, 5, 5, 6, 2, 4, 2, 7, 3, 6, 2, 5, -1, 7, 3, -1, 2, 15, 2, 3, 6, 8, 3, 4, 2, 7, 3, 4, 2, 14, 2, 5, 7, 8, 2, 6, 4, 3, 4, 9, 2, 13, 3, 5, 3, 4, 2, 11, 2, 9, 3, 4, 3, 12, 2, 5, 4, 6, 2, 9, 2, 5, 5, 5, 3, 11, 2, 7, 5, 6, 2, 6, 3, 9, 7, 7, 2, 10, 4, 6, 4, 4, -1, 9, 2, 3

Offset: 1

Author

Michael Gerenrot (sch116(AT)yahoo.com)

Keywords

• sign

Comments

Length of transient part of trajectory of n if trajectory reaches 1, otherwise a(n) = -1. See A098008 for another version. See A098007 for further information.

References

• R. K. Guy, Unsolved Problems in Number Theory, B6.
• R. K. Guy and J. L. Selfridge, Interim report on aliquot series, pp. 557-580 of Proceedings Manitoba Conference on Numerical Mathematics. University of Manitoba, Winnipeg, Oct 1971.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..275

Crossrefs

Cf. A098008, A098007, A044050, A003023.

Programs

Scheme

(define (A007906 n) (let loop ((visited (list n)) (i 1)) (let ((next (A001065 (car visited)))) (cond ((zero? next) i) ((member next visited) -1) (else (loop (cons next visited) (+ 1 i)))))))
(define (A001065 n) (- (A000203 n) n)) ;; For an implementation of A000203, see under that entry.
;; Antti Karttunen, Nov 02 2017

Extensions

Definition changed by N. J. A. Sloane, Nov 02 2017 at the suggestion of Antti Karttunen.