On asymptotic properties of aliquot sequences

Author:
P. Erdős

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

MSC:
Primary 10A20

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 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****[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**, 10.1090/S0025-5718-1975-0384669-X**[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 H]**H. J. J. te Riele,*A note on the Catalan-Dickson conjecture*, Math. Comp.**27**(1973), 189–192. MR**0325522**, 10.1090/S0025-5718-1973-0325522-5

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

Article copyright:
© Copyright 1976
American Mathematical Society