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A353617
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Decimal expansion of the asymptotic median of the abundancy indices of the positive integers.
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2
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OFFSET
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1,2
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COMMENTS
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The abundancy index of a number k is sigma(k)/k = A017665(k)/A017666(k), where sigma is the sum-of-divisors function (A000203).
Davenport (1933) proved that sigma(k)/k possesses a continuous distribution function. Therefore, it has an asymptotic median.
The asymptotic mean of the abundancy indices is Pi^2/6 = 1.64493... (A013661).
Mitsuo Kobayashi (unpublished, 2018) found that the median is in the interval (1.523812, 1.5238175) (see the MathOverflow link).
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REFERENCES
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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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EXAMPLE
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1.52381...
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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