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%I #10 May 01 2022 07:56:29
%S 1,5,2,3,8,1
%N Decimal expansion of the asymptotic median of the abundancy indices of the positive integers.
%C The abundancy index of a number k is sigma(k)/k = A017665(k)/A017666(k), where sigma is the sum-of-divisors function (A000203).
%C Davenport (1933) proved that sigma(k)/k possesses a continuous distribution function. Therefore, it has an asymptotic median.
%C The asymptotic mean of the abundancy indices is Pi^2/6 = 1.64493... (A013661).
%C Mitsuo Kobayashi (unpublished, 2018) found that the median is in the interval (1.523812, 1.5238175) (see the MathOverflow link).
%D Harold Davenport, Über numeri abundantes, Sitzungsberichte der Preußischen Akademie der Wissenschaften, phys.-math. Klasse, No. 6 (1933), pp. 830-837.
%H Sébastien Palcoux, <a href="https://mathoverflow.net/questions/364542/on-the-density-map-of-the-abundancy-index">On the density map of the abundancy index</a>, MathOverflow, 2020.
%e 1.52381...
%Y Cf. A000203, A013661, A017665, A017666, A302991, A353615, A353616.
%K nonn,cons,more
%O 1,2
%A _Amiram Eldar_, Apr 30 2022