A088818 Numbers k whose abundance-radius does not exceed log(log(k)), i.e., abs(sigma(k)-2*k) <= log(log(k)).

6, 16, 28, 32, 64, 128, 256, 496, 512, 1024, 1952, 2048, 4096, 8128, 8192, 16384, 32768, 32896, 65536, 130304, 131072, 262144, 522752, 524288, 1048576, 2097152, 4194304, 8382464, 8388608, 16777216, 33550336, 33554432, 67108864, 134193152, 134217728, 268435456

Offset: 1

Author

Labos Elemer, Oct 20 2003

Keywords

• nonn

Examples

			The perfect numbers are all terms.
It is an infinite sequence since it includes all the powers of 2 (A000079) that are larger than 8 (as almost-perfect numbers).
		

Crossrefs

Cf. A033880, A088009, A088010, A088011, A088012, A077374, A000396, A000079.

Programs

Mathematica

abu[x_] := Abs[DivisorSigma[1, x]-2*x]; Do[If[ !Greater[abu[n], Log[Log[n]]//N], Print[n]], {n, 1, 1000000}]

PARI

is(n) = n > 1 && abs(sigma(n)-2*n) < log(log(n)); \\ Amiram Eldar, Jul 24 2024

Extensions

a(28)-a(34) from Donovan Johnson, Dec 21 2008

a(35)-a(36) from Amiram Eldar, Jul 24 2024