cp's OEIS Frontend

A088833 Numbers n whose abundance is 8: sigma(n) - 2n = 8.

%I A088833 #41 Apr 07 2025 07:51:37
%S A088833 56,368,836,11096,17816,45356,77744,91388,128768,254012,388076,
%T A088833 2087936,2291936,13174976,29465852,35021696,45335936,120888092,
%U A088833 260378492,381236216,775397948,3381872252,4856970752,6800228816,8589344768,44257207676,114141404156
%N A088833 Numbers n whose abundance is 8: sigma(n) - 2n = 8.
%C A088833 A subset of A045770.
%C A088833 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 A088833 a(28) > 10^12. - _Donovan Johnson_, Dec 08 2011
%C A088833 a(31) > 10^13. - _Giovanni Resta_, Mar 29 2013
%C A088833 a(38) > 10^18. - _Hiroaki Yamanouchi_, Aug 23 2018
%C A088833 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 A088833 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 A088833 Except first 4 terms of A045770 (1, 7, 10, and 49) are here: abundances = {-1,-6,-2,-41,8,8,8,8,8,8,8,8,8,8,8,8,8}.
%t A088833 Do[If[DivisorSigma[1,n]==2n+8,Print[n]],{n,100000000}] (* _Farideh Firoozbakht_, Feb 15 2008 *)
%o A088833 (PARI) is(n)=sigma(n)==2*n+8 \\ _Charles R Greathouse IV_, Feb 21 2017
%Y A088833 Cf. A033880, A045668, A045669, A045770, A088831, A088832, A059610, A125247 (deficiency 8).
%K A088833 nonn
%O A088833 1,1
%A A088833 _Labos Elemer_, Oct 28 2003
%E A088833 a(14)-a(17) from _Farideh Firoozbakht_, Feb 15 2008
%E A088833 a(18)-a(25) from _Donovan Johnson_, Dec 23 2008
%E A088833 a(26)-a(27) from _Donovan Johnson_, Dec 08 2011