A088818 - OEIS

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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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..36.

EXAMPLE

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).

MATHEMATICA

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

PROG

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