On asymptotic properties of aliquot sequences
Author:
P. Erdős
Journal:
Math. Comp. 30 (1976), 641645
MSC:
Primary 10A20
MathSciNet review:
0404115
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: Put . . In this note we prove that for every k the density of integers satisfying is 1. Several unsolved problems are stated.
 [1]
E. CATALAN, Bull. Soc. Math. France, v. 16, 1887/88, pp. 128129.
 [2]
L. E. DICKSON, "Theorems and tables on the sum of the divisors of a number," Quart. J. Math., v. 44, 1913, pp. 264296.
 [3]
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
(49 #194)
 [4]
Richard
K. Guy and J.
L. Selfridge, What drives an aliquot
sequence?, Math. Comput. 29 (1975), 101–107.
Collection of articles dedicated to Derrick Henry Lehmer on the occasion of
his seventieth birthday. MR 0384669
(52 #5542), http://dx.doi.org/10.1090/S0025571819750384669X
 [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
(50 #4455)
 [6 H]
H.
J. J. te Riele, A note on the CatalanDickson
conjecture, Math. Comp. 27 (1973), 189–192. MR 0325522
(48 #3869), http://dx.doi.org/10.1090/S00255718197303255225
 [1]
 E. CATALAN, Bull. Soc. Math. France, v. 16, 1887/88, pp. 128129.
 [2]
 L. E. DICKSON, "Theorems and tables on the sum of the divisors of a number," Quart. J. Math., v. 44, 1913, pp. 264296.
 [3]
 RICHARD K. GUY & J. L. SELFRIDGE, "Interim report on aliquot series," Proc. Manitoba Conf. Numerical Math. (Univ. Manitoba, Winnipeg, Man., 1971), Dept. Comput. Sci., Univ. Manitoba, Winnipeg, Man., 1971, pp. 557580. MR 49 #194. MR 0335412 (49:194)
 [4]
 RICHARD K. GUY & J. L. SELFRIDGE, "What drives an aliquot sequence?," Math. Comp., v. 29, 1975, pp. 101107. MR 0384669 (52:5542)
 [5]
 RICHARD K. GUY, D. H. LEHMER, J. L. SELFRIDGE & M. C. WUNDERLICH, "Second report on aliquot sequences," Proc. Third Manitoba Conf. Numerical Math. (Winnipeg, Man., 1973), Utilitas Math., Winnipeg, Man., 1974, pp. 357368. MR 50 #4455. MR 0351967 (50:4455)
 [6 H]
 J. J. te RIELE, "A note on the CatalanDickson conjecture," Math. Comp., v. 27, 1973, pp. 189192. MR 48 #3869. MR 0325522 (48:3869)
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
10A20
Retrieve articles in all journals
with MSC:
10A20
Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197604041158
PII:
S 00255718(1976)04041158
Article copyright:
© Copyright 1976
American Mathematical Society
