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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 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.)