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.*, v. 24, 1970, pp. 423-429. MR**42**#5887. MR**0271004 (42:5887)****[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 & J. L. SELFRIDGE, "Interim report on aliquot series,"*Proc. Manitoba Conf. Numerical Math.*, Winnipeg, 1971, pp. 557-580. MR**0335412 (49:194)****[5]**RICHARD K. GUY, D. H. LEHMER, J. L. SELFRIDGE & M. C. WUNDERLICH, "Second report on aliquot sequences,"*Proc.*3*rd Manitoba Conf. Numerical Math.*, Winnipeg, 1973, pp. 357-368. MR**0351967 (50:4455)****[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