%I #9 May 03 2013 20:56:31
%S 1,3,7,14,31,127,206,532,954,957,1334,1364,1634,2685,2974,4364,8191,
%T 14841,18873,19358,20145,24957,33998,36566,42818,56564,64665,74918,
%U 79826,79833,84134,92685,104944,109214,111506,116937,122073,131071,138237,147454,161001
%N Numbers n such that sigma(n+1) - sigma(n) = k*n for some integer k, where sigma(n) = A000203 (sum of divisors of n).
%C Supersequence of A000668 for k=1 (Mersenne primes), A067803 for k=-1 (numbers n such that sigma(n) - sigma(n+1) = n) and A002961 for k=0 (numbers n such that n and n+1 have same sum of divisors). For number 1 is k=2.
%C Corresponding values of integers k: 2, 1, 1, 0, 1, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,....
%H Donovan Johnson, <a href="/A223136/b223136.txt">Table of n, a(n) for n = 1..1000</a>
%e Number 532 is in sequence because sigma(533) - sigma(532) = 588 - 1120 = -532 = (-1) * 532; k = -1.
%t Select[Range[10000], IntegerQ[(DivisorSigma[1, # + 1] - DivisorSigma[1, #])/#] &] (* _T. D. Noe_, May 02 2013 *)
%Y Cf. A000668, A067803, A002961, A000203.
%K nonn
%O 1,2
%A _Jaroslav Krizek_, May 01 2013
%E Extended by _T. D. Noe_, May 02 2013