

A322287


The number of odd abundant numbers below 10^n.


0



0, 0, 1, 23, 210, 1996, 20661, 205366, 2048662, 20502004, 204951472
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OFFSET

1,4


COMMENTS

Anderson proved that the density of odd deficient numbers is at least (48  3*Pi^2)/(32  Pi^2) ~ 0.831...
Kobayashi et al. proved that the density of odd abundant numbers is between 0.002042 and 0.002071.


LINKS

Table of n, a(n) for n=1..11.
C. W. Anderson, Density of Deficient Odd Numbers, The American Mathematical Monthly, Vol. 82, No. 10 (1975), pp. 10181020.
Mitsuo Kobayashi, Paul Pollack and Carl Pomerance, On the distribution of sociable numbers, Journal of Number Theory, Vol. 129, No. 8 (2009), pp. 19902009. See Theorem 10 on p. 2007.


FORMULA

Lim_{n>oo} a(n)/10^n = 0.0020... is the density of odd abundant numbers.


EXAMPLE

945 is the only odd abundant number below 10^3, thus a(3) = 1.


MATHEMATICA

abQ[n_] := DivisorSigma[1, n] > 2 n; c = 0; k = 1; s = {}; Do[While[k < 10^n, If[abQ[k], c++]; k += 2]; AppendTo[s, c], {n, 1, 5}]; s


CROSSREFS

Cf. A000203, A005231, A302992, A302993, A302994, A307820, A307821, A307823.
Sequence in context: A042020 A263521 A084428 * A327918 A327919 A165243
Adjacent sequences: A322284 A322285 A322286 * A322288 A322289 A322290


KEYWORD

nonn,more


AUTHOR

Amiram Eldar, Aug 28 2019


STATUS

approved



