A088011 Even and odd solutions to abs(sigma(x)-2x) <= log(x). Numbers n whose abundance-radius does not exceed log(n).

4, 6, 8, 10, 16, 20, 28, 32, 64, 70, 88, 104, 110, 128, 136, 152, 256, 464, 496, 512, 592, 650, 884, 1024, 1155, 1888, 1952, 2048, 2144, 4030, 4096, 5830, 8128, 8192, 8384, 8925, 11096, 16384, 17816, 18632, 18904, 32128, 32445, 32768, 32896, 33664, 45356

Offset: 1

Author

Labos Elemer, Oct 20 2003

Keywords

• nonn

Comments

See A088012 for the subsequence of odd terms, only 7 being known up to 10^13. - M. F. Hasler, Feb 21 2017

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

(is(n)=abs(sigma(n)-2*n)M. F. Hasler, Feb 21 2017