A353617 Decimal expansion of the asymptotic median of the abundancy indices of the positive integers.

1, 5, 2, 3, 8, 1

Offset: 1

Author

Amiram Eldar, Apr 30 2022

Keywords

• nonn
• cons
• more

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Mitsuo Kobayashi (unpublished, 2018) found that the median is in the interval (1.523812, 1.5238175) (see the MathOverflow link).

Examples

			1.52381...
		

References

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

Links

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

Crossrefs

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