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A302991 Decimal expansion of the asymptotic density of abundant numbers. 13
2, 4, 7, 6, 1, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
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).
REFERENCES
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.
LINKS
Felix Behrend, Über numeri abundantes, inaugural dissertation, Sitzungsberichte der Preußischen Akademie der Wissenschaften, phys.-math. Klasse, pp. 280-293, 1933.
Marc Deléglise, Bounds for the Density of Abundant Integers, Experimental Mathematics, Vol. 7, No. 2 (1998), pp. 137-143.
Mitsuo Kobayashi, On the Density of Abundant Numbers, Ph.D. thesis, Dartmouth College, 2010.
H. Salié, Über die Dichte abundanter Zahlen, Mathematische Nachrichten, Vol. 14, No. 1 (1955), pp. 39-46.
Charles R. Wall, Phillip L. Crews and Donald B. Johnson, Density Bounds for the Sum of Divisors Function, Mathematics of Computation, Vol. 26, No. 119 (1972), pp. 773-777; Errata, Vol. 31, No. 138 (1977), p. 616.
EXAMPLE
0.2476...
CROSSREFS
Sequence in context: A244591 A299324 A261076 * A015791 A335818 A129980
KEYWORD
nonn,cons,more
AUTHOR
Amiram Eldar, Apr 17 2018
EXTENSIONS
a(4)-a(5) from Muniru A Asiru, Aug 20 2018
STATUS
approved

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Last modified March 28 10:31 EDT 2024. Contains 371240 sequences. (Running on oeis4.)