On asymptotic properties of aliquot sequences

Author:
P. Erdős

Journal:
Math. Comp. **30** (1976), 641-645

MSC:
Primary 10A20

DOI:
https://doi.org/10.1090/S0025-5718-1976-0404115-8

MathSciNet review:
0404115

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Abstract: Put . . In this note we prove that for every *k* the density of integers satisfying

**[1]**E. CATALAN,*Bull. Soc. Math. France*, v. 16, 1887/88, pp. 128-129.**[2]**L. E. DICKSON, "Theorems and tables on the sum of the divisors of a number,"*Quart. J. Math.*, v. 44, 1913, pp. 264-296.**[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. 557-580. 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. 101-107. 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. 357-368. MR**50**#4455. MR**0351967 (50:4455)****[6 H]**J. J. te RIELE, "A note on the Catalan-Dickson conjecture,"*Math. Comp.*, v. 27, 1973, pp. 189-192. MR**48**#3869. MR**0325522 (48:3869)**

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DOI:
https://doi.org/10.1090/S0025-5718-1976-0404115-8

Article copyright:
© Copyright 1976
American Mathematical Society