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Even and odd solutions to abs(sigma(x)-2x) <= log(x). Numbers n whose abundance-radius does not exceed log(n).
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%I #15 Sep 21 2019 08:25:51

%S 4,6,8,10,16,20,28,32,64,70,88,104,110,128,136,152,256,464,496,512,

%T 592,650,884,1024,1155,1888,1952,2048,2144,4030,4096,5830,8128,8192,

%U 8384,8925,11096,16384,17816,18632,18904,32128,32445,32768,32896,33664,45356

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

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

%H Amiram Eldar, <a href="/A088011/b088011.txt">Table of n, a(n) for n = 1..10000</a>

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

%o (PARI) (is(n)=abs(sigma(n)-2*n)<log(n)); select(is,[1..5000]) \\ _M. F. Hasler_, Feb 21 2017

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

%K nonn

%O 1,1

%A _Labos Elemer_, Oct 20 2003