On asymptotic properties of aliquot sequences
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- by P. Erdős PDF
- Math. Comp. 30 (1976), 641-645 Request permission
Abstract:
Put ${s^{(1)}}(n) = \sigma (n) - n,\sigma (n) = {\Sigma _{d/n}}d$. ${s^k}(n) = {s^{(1)}}({s^{(k - 1)}}(n))$. In this note we prove that for every k the density of integers satisfying \[ {s^k}(n) = (1 + \sigma (1))n{((\sigma (n) - n)/n)^k}\] is 1. Several unsolved problems are stated.References
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Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Math. Comp. 30 (1976), 641-645
- MSC: Primary 10A20
- DOI: https://doi.org/10.1090/S0025-5718-1976-0404115-8
- MathSciNet review: 0404115