OFFSET
0,1
COMMENTS
The satellite problem: sigma(x)=2x+odd seems much more difficult.
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).
a(221) <= 576460514469609472. - Donovan Johnson, Jan 06 2014
LINKS
Donovan Johnson, Table of n, a(n) for n = 0..220
Nichole Davis, Dominic Klyve and Nicole Kraght, On the difference between an integer and the sum of its proper divisors, Involve, Vol. 6 (2013), No. 4, 493-504; DOI: 10.2140/involve.2013.6.493.
EXAMPLE
n=67: 2n=134, first solution to sigma(x)=2x+134 is a(67)=1958912;
n=0: solution is the least perfect number, a(0)=6;
2n=12, 2n=56 provide large number of solutions.
MATHEMATICA
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Oct 13 2003
EXTENSIONS
a(47) corrected by Donovan Johnson, Jan 06 2014
STATUS
approved