A088008 Solutions to sigma(x) - 2x <= x^(1/3), both even and odd. Abundance-radius = abs(sigma(n)-2n) does not exceed 3rd root of n.

1, 2, 4, 6, 8, 10, 16, 20, 28, 32, 64, 70, 88, 104, 110, 128, 136, 152, 256, 315, 464, 496, 512, 592, 650, 836, 884, 1012, 1024, 1155, 1696, 1758, 1842, 1866, 1878, 1888, 1902, 1952, 1986, 2022, 2048, 2082, 2094, 2118, 2144, 2154, 2202, 2238, 2272, 2274, 2298

Offset: 1

Author

Labos Elemer, Oct 20 2003

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A077374, A088007-A088012, A000396, A000079, A005100, A005101.

Programs

Mathematica

abu[x_] := Abs[DivisorSigma[1, x]-2*x] Do[If[ !Greater[abu[n], n^(1/3)//N], Print[n]], {n, 1, 100000}]
Select[Range[2300],Abs[DivisorSigma[1,#]-2#]<=CubeRoot[#]&] (* Harvey P. Dale, Feb 22 2023 *)