A088833 - OEIS

%I #38 Aug 23 2018 10:25:27

%S 56,368,836,11096,17816,45356,77744,91388,128768,254012,388076,

%T 2087936,2291936,13174976,29465852,35021696,45335936,120888092,

%U 260378492,381236216,775397948,3381872252,4856970752,6800228816,8589344768,44257207676,114141404156

%N Numbers n whose abundance is 8: sigma(n) - 2n = 8.

%C A subset of A045770.

%C If p=2^m-9 is prime (m is in the sequence A059610) then n=2^(m-1)*p is in the sequence. See comment lines of the sequence A088831. 56, 368, 128768, 2087936 & 8589344768 are of the mentioned form. - _Farideh Firoozbakht_, Feb 15 2008

%C a(28) > 10^12. - _Donovan Johnson_, Dec 08 2011

%C a(31) > 10^13. - _Giovanni Resta_, Mar 29 2013

%C a(38) > 10^18. - _Hiroaki Yamanouchi_, Aug 23 2018

%C Any term x of this sequence can be combined with any term y of A125247 to satisfy the property (sigma(x)+sigma(y))/(x+y) = 2, which is a necessary (but not sufficient) condition for two numbers to be amicable. - _Timothy L. Tiffin_, Sep 13 2016

%H Giovanni Resta and Hiroaki Yamanouchi, <a href="/A088833/b088833.txt">Table of n, a(n) for n = 1..37</a> (terms a(1)-a(30) from _Giovanni Resta_)

%e Except first 2 terms of A045770 (10 and 49) are here:abundances={-2,-41,8,8,8,8,8,8,8,8,8,8,8,8,8}.

%t Do[If[DivisorSigma[1,n]==2n+8,Print[n]],{n,100000000}] (* _Farideh Firoozbakht_, Feb 15 2008 *)

%o (PARI) is(n)=sigma(n)==2*n+8 \\ _Charles R Greathouse IV_, Feb 21 2017

%Y Cf. A033880, A045668, A045669, A088831, A088832, A059610, A125247 (deficiency 8).

%K nonn

%O 1,1

%A _Labos Elemer_, Oct 28 2003

%E a(14)-a(17) from _Farideh Firoozbakht_, Feb 15 2008

%E a(18)-a(25) from _Donovan Johnson_, Dec 23 2008

%E a(26)-a(27) from _Donovan Johnson_, Dec 08 2011