What drives an aliquot sequence?
Authors:
Richard K. Guy and J. L. Selfridge
Journal:
Math. Comp. 29 (1975), 101107
MSC:
Primary 10A20; Secondary 10A40
Corrigendum:
Math. Comp. 34 (1980), 319321.
MathSciNet review:
0384669
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Abstract 
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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.
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Henri
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L. E. DICKSON, "Theorems and tables on the sums of divisors of a number," Quart. J. Math., v. 44, 1913, pp. 264296.
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Richard
K. Guy and J.
L. Selfridge, Interim report on aliquot series, Proceedings of
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pp. 557–580. MR 0335412
(49 #194)
 [5]
Richard
K. Guy, D.
H. Lehmer, J.
L. Selfridge, and M.
C. Wunderlich, Second report on aliquot sequences, (Winnipeg,
Man., 1973) Utilitas Math., Winnipeg, Man., 1974, pp. 357–368.
MR
0351967 (50 #4455)
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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. 807809.
 [8]
P. POULET, L'Intermédiaire des Math., v. 25, 1918, pp. 100101.
 [1]
 E. CATALAN, Bull. Soc. Math. France, v. 16, 1887/88, pp. 128129.
 [2]
 HENRI COHEN, "On amicable and sociable numbers," Math. Comp., v. 24, 1970, pp. 423429. 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. 264296.
 [4]
 RICHARD K. GUY & J. L. SELFRIDGE, "Interim report on aliquot series," Proc. Manitoba Conf. Numerical Math., Winnipeg, 1971, pp. 557580. MR 0335412 (49:194)
 [5]
 RICHARD K. GUY, D. H. LEHMER, J. L. SELFRIDGE & M. C. WUNDERLICH, "Second report on aliquot sequences," Proc. 3rd Manitoba Conf. Numerical Math., Winnipeg, 1973, pp. 357368. 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. 807809.
 [8]
 P. POULET, L'Intermédiaire des Math., v. 25, 1918, pp. 100101.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025571819750384669X
PII:
S 00255718(1975)0384669X
Keywords:
Aliquot sequence,
guide,
driver,
perfect number,
amicable pair,
Poulet cycle,
CatalanDickson conjecture
Article copyright:
© Copyright 1975 American Mathematical Society
