This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A223136 #9 May 03 2013 20:56:31 %S A223136 1,3,7,14,31,127,206,532,954,957,1334,1364,1634,2685,2974,4364,8191, %T A223136 14841,18873,19358,20145,24957,33998,36566,42818,56564,64665,74918, %U A223136 79826,79833,84134,92685,104944,109214,111506,116937,122073,131071,138237,147454,161001 %N A223136 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 A223136 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 A223136 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 A223136 Donovan Johnson, <a href="/A223136/b223136.txt">Table of n, a(n) for n = 1..1000</a> %e A223136 Number 532 is in sequence because sigma(533) - sigma(532) = 588 - 1120 = -532 = (-1) * 532; k = -1. %t A223136 Select[Range[10000], IntegerQ[(DivisorSigma[1, # + 1] - DivisorSigma[1, #])/#] &] (* _T. D. Noe_, May 02 2013 *) %Y A223136 Cf. A000668, A067803, A002961, A000203. %K A223136 nonn %O A223136 1,2 %A A223136 _Jaroslav Krizek_, May 01 2013 %E A223136 Extended by _T. D. Noe_, May 02 2013