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A087998 a(n) = smallest number x such that sigma(x) = 2x + 2n. 5

%I

%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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Last modified February 7 14:16 EST 2023. Contains 360123 sequences. (Running on oeis4.)