Primitive $\alpha$-abundant numbers
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- by Graeme L. Cohen PDF
- Math. Comp. 43 (1984), 263-270 Request permission
Abstract:
A number N is primitive $\alpha$-abundant if $\sigma (M)/M < \alpha \leqslant \sigma (N)/N$ for all proper divisors M of N. In this paper, we tabulate, for $1 < \alpha \leqslant 5.4$, all such N for which $\sigma (N)/N$ is greatest. We show that, if N is primitive $\alpha$-abundant and $\alpha > 1.6$, then $\sigma (N)/N < \alpha + \min \{ \frac {2}{5},3\alpha /2{e^{5\alpha /9}}\}$.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Math. Comp. 43 (1984), 263-270
- MSC: Primary 11A25
- DOI: https://doi.org/10.1090/S0025-5718-1984-0744936-X
- MathSciNet review: 744936