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A322287 The number of odd abundant numbers below 10^n. 0
0, 0, 1, 23, 210, 1996, 20661, 205366, 2048662, 20502004, 204951472 (list; graph; refs; listen; history; text; internal format)
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. 1018-1020.

Mitsuo Kobayashi, Paul Pollack and Carl Pomerance, On the distribution of sociable numbers, Journal of Number Theory, Vol. 129, No. 8 (2009), pp. 1990-2009. 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

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Last modified June 5 00:50 EDT 2020. Contains 334828 sequences. (Running on oeis4.)