%I
%S 1,2,3,4,6,7,16,28,31,38,127,256,278,469,1298,3477,7298,7525,8191,
%T 13969,19909,26738,31492,65536,99381,131071,357698,524287,20742482,
%U 33550336,772499089,1959272066
%N Numbers n such that the sum of the proper divisors of n and n+1 equals either n or n+1.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AliquotDivisor.html">Aliquot Divisor./</a>.
%e 16 has the proper divisors 1,2,4 and 8. 17 has the proper divisor 1. The sum of those divisors is 16, therefore 16 is in the sequence.
%t Select[Range[1000000], DivisorSigma[1, # ] + DivisorSigma[1, # + 1]  2*#  1 == #  DivisorSigma[1, # ] + DivisorSigma[1, # + 1]  2*#  1 == # + 1 &]
%t lst = {}; d1 = d2 = 1; Do[ d2 = DivisorSigma[1, n + 1]; d = d1 + d2  2 n  1; If[d == n  d == n + 1, Print@n; AppendTo[lst, n]]; d1 = d2, {n, 2*10^9}]; lst (* _Robert G. Wilson v_ *)
%K nonn
%O 1,2
%A _J. M. Bergot_, Jul 14 2007
%E Edited, corrected and extended by _Stefan Steinerberger_, Jul 16 2007
%E a(29)  a(32) from _Robert G. Wilson v_, Jul 27 2007
