A088007 Numbers n such that abs(sigma(n) - 2n) <= sqrt(n).

1, 2, 4, 6, 8, 10, 16, 18, 20, 28, 32, 44, 50, 52, 64, 70, 88, 104, 110, 128, 130, 136, 152, 174, 184, 186, 196, 222, 232, 246, 256, 258, 272, 282, 304, 315, 318, 354, 366, 368, 402, 426, 438, 464, 474, 496, 498, 512, 534, 550, 582, 592, 606, 618, 642, 650, 654

Offset: 1

Author

Labos Elemer, Oct 20 2003

Keywords

• nonn

Comments

Abundance-radius = abs(sigma(n)-2n) does not exceed square root.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A077374, A088008-A088012, A000396, A000079, A005100, A005101.

Programs

Mathematica

abu[x_] := Abs[DivisorSigma[1, x]-2*x] Do[If[ !Greater[abu[n], Sqrt[n]//N], Print[n]], {n, 1, 100000}]

PARI

is(n)=abs(sigma(n)-2*n)<=sqrtint(n) \\ Charles R Greathouse IV, Mar 09 2014

Extensions

New name from Charles R Greathouse IV, Mar 09 2014