A353617 - OEIS

A353617

Decimal expansion of the asymptotic median of the abundancy indices of the positive integers.

1, 5, 2, 3, 8, 1

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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Mitsuo Kobayashi (unpublished, 2018) found that the median is in the interval (1.523812, 1.5238175) (see the MathOverflow link).

REFERENCES

Harold Davenport, Über numeri abundantes, Sitzungsberichte der Preußischen Akademie der Wissenschaften, phys.-math. Klasse, No. 6 (1933), pp. 830-837.

LINKS

Table of n, a(n) for n=1..6.

Sébastien Palcoux, On the density map of the abundancy index, MathOverflow, 2020.

EXAMPLE

1.52381...

CROSSREFS

Cf. A000203, A013661, A017665, A017666, A302991, A353615, A353616.

Sequence in context: A200301 A114746 A364456 * A133746 A374957 A176319

Adjacent sequences: A353614 A353615 A353616 * A353618 A353619 A353620

KEYWORD

nonn,cons,more

AUTHOR

Amiram Eldar, Apr 30 2022

STATUS

approved