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A302991
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Decimal expansion of the asymptotic density of abundant numbers.
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13
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OFFSET
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0,1
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COMMENTS
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The existence of this density was asked about by Erich Bessel-Hagen in 1929 and was proved by Harold Davenport in 1933.
Previous evaluated bounds on the value of density, D, were D < 0.47 (Behrend, 1932), 0.241 < D < 0.314 (Behrend, 1933), 0.24432 < D (Salié, 1955), 0.2441 < D < 0.2909 (Wall et al., 1972), and 0.2474 < D < 0.2480 (Deléglise, 1988); the current bounds are 0.2476171 < D < 0.2476475 (Kobayashi, 2010).
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REFERENCES
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Felix Behrend, Über numeri abundantes I, S.-Ber. Preuß. Akad. Wiss., math.-nat. Kl. (1932), pp. 322-328.
Erich Bessel-Hagen, Repertorium der höheren Mathematik, 2nd edn., Vol. 1, B. G. Teubner (Leipzig, 1929), pp. 1458-1574.
Harold Davenport, Über numeri abundantes, Sitzungsberichte der Preußischen Akademie der Wissenschaften, phys.-math. Klasse, No. 6 (1933), pp. 830-837.
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LINKS
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Felix Behrend, Über numeri abundantes, inaugural dissertation, Sitzungsberichte der Preußischen Akademie der Wissenschaften, phys.-math. Klasse, pp. 280-293, 1933.
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EXAMPLE
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0.2476...
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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