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

 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 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

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.

Last modified August 7 10:34 EDT 2024. Contains 375011 sequences. (Running on oeis4.)