login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A322287 The number of odd abundant numbers below 10^n. 3
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
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
Sequence in context: A042020 A263521 A084428 * A327918 A327919 A165243
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Aug 28 2019
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 14:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)