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

DOI:
https://doi.org/10.1090/S0025-5718-1975-0384669-X

Corrigendum:
Math. Comp. **34** (1980), 319-321.

MathSciNet review:
0384669

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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.

**[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**, https://doi.org/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.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1975-0384669-X

Keywords:
Aliquot sequence,
guide,
driver,
perfect number,
amicable pair,
Poulet cycle,
Catalan-Dickson conjecture

Article copyright:
© Copyright 1975
American Mathematical Society