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%I #18 Aug 03 2016 03:35:34
%S 6,20,12,8925,56,40,24,272,550,208,176,1312,112,80,48,945,572,928,
%T 2205,5696,736,9555,350,490,60,416,352,90,84,160,96,24704,108,3904,
%U 260,487936,132,1575,340,234,156,22144,2752,2624,460,306,500,475648,204
%N a(n) = smallest number x such that sigma(x) = 2x + 2n.
%C The satellite problem: sigma(x)=2x+odd seems much more difficult.
%C Solutions (square or twice a square!) obtained only for: 3,7,17,19,31,39,41,51,59,65,71,89,115,119,127,161,185,199 (see A140863).
%C a(221) <= 576460514469609472. - _Donovan Johnson_, Jan 06 2014
%H Donovan Johnson, <a href="/A087998/b087998.txt">Table of n, a(n) for n = 0..220</a>
%H Nichole Davis, Dominic Klyve and Nicole Kraght, <a href="http://dx.doi.org/10.2140/involve.2013.6.493">On the difference between an integer and the sum of its proper divisors</a>, Involve, Vol. 6 (2013), No. 4, 493-504; DOI: 10.2140/involve.2013.6.493.
%e n=67: 2n=134, first solution to sigma(x)=2x+134 is a(67)=1958912;
%e n=0: solution is the least perfect number, a(0)=6;
%e 2n=12, 2n=56 provide large number of solutions.
%t ds[x_, de_] := DivisorSigma[1, x]-2*x-de a[n_] := Block[{m=1, s=ds[m, n]}, While[(s !=0)&& !Greater[m, 10000000], m++ ]; m]; Table[a[n], {n, 1, 100}]//Timing
%K nonn
%O 0,1
%A _Labos Elemer_, Oct 13 2003
%E a(47) corrected by _Donovan Johnson_, Jan 06 2014
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