Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



What drives an aliquot sequence?

Authors: Richard K. Guy and J. L. Selfridge
Journal: Math. Comp. 29 (1975), 101-107
MSC: Primary 10A20; Secondary 10A40
Corrigendum: Math. Comp. 34 (1980), 319-321.
MathSciNet review: 0384669
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The concept of the "driver" of an aliquot sequence is discussed. It is shown that no driver can be expected to persist indefinitely. A definition of driver is given which leads to just 5 drivers apart from the even perfect numbers.

References [Enhancements On Off] (What's this?)

  • [1] E. CATALAN, Bull. Soc. Math. France, v. 16, 1887/88, pp. 128-129.
  • [2] Henri Cohen, On amicable and sociable numbers, Math. Comp. 24 (1970), 423–429. MR 0271004, 10.1090/S0025-5718-1970-0271004-6
  • [3] L. E. DICKSON, "Theorems and tables on the sums of divisors of a number," Quart. J. Math., v. 44, 1913, pp. 264-296.
  • [4] Richard K. Guy and J. L. Selfridge, Interim report on aliquot series, Proceedings of the Manitoba Conference on Numerical Mathematics (Univ. Manitoba, Winnipeg, Man., 1971) Dept. Comput. Sci., Univ. Manitoba, Winnipeg, Man., 1971, pp. 557–580. MR 0335412
  • [5] Richard K. Guy, D. H. Lehmer, J. L. Selfridge, and M. C. Wunderlich, Second report on aliquot sequences, Proceedings of the Third Manitoba Conference on Numerical Mathematics (Winnipeg, Man., 1973) Utilitas Math., Winnipeg, Man., 1974, pp. 357–368. MR 0351967
  • [6] RICHARD K. GUY & J. L. SELFRIDGE, Combined Report on Aliquot Sequences, University of Calgary Math. Research Report No. 225, May 1974.
  • [7] G. AARON PAXSON, "Aliquot sequences (preliminary report)," Amer. Math. Monthly, v. 63, 1956, p. 614; Math. Comp., v. 26, 1972, pp. 807-809.
  • [8] P. POULET, L'Intermédiaire des Math., v. 25, 1918, pp. 100-101.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 10A20, 10A40

Retrieve articles in all journals with MSC: 10A20, 10A40

Additional Information

Keywords: Aliquot sequence, guide, driver, perfect number, amicable pair, Poulet cycle, Catalan-Dickson conjecture
Article copyright: © Copyright 1975 American Mathematical Society