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 A223137 #8 May 03 2013 20:56:41 %S A223137 5,34,55,285,367,835,849,919,1241,1505,2911,2914,3305,4149,4188,6111, %T A223137 6903,7170,7913,9360,10251,10541,12566,15086,17273,17815,19005,19689, %U A223137 21411,21462,24882,25020,26610,28125,30593,30789,31485,38211,38983,39787,40311,45355 %N A223137 Numbers n such that sigma(n+1) - sigma(n-1) = k*n for some integer k, where sigma(n) = A000203 (sum of divisors of n). %C A223137 Supersequence of A055574 for k=0 (n satisfying sigma(n+1) = sigma(n-1)). For number 5 is k=1. Are there other such number for k=1 or k=-1? %C A223137 Corresponding values of integers k: 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,.... %H A223137 Donovan Johnson, <a href="/A223137/b223137.txt">Table of n, a(n) for n = 1..1000</a> %e A223137 Number 5 is in sequence because sigma(6) - sigma(4) = 12 - 7 = 5 = 1 * 5; k=1. %t A223137 Select[Range[100000], IntegerQ[(DivisorSigma[1, # + 1] - DivisorSigma[1, # - 1])/#] &] (* _T. D. Noe_, May 02 2013 *) %Y A223137 Cf. A055574, A000203. %K A223137 nonn %O A223137 1,1 %A A223137 _Jaroslav Krizek_, May 01 2013 %E A223137 Extended by _T. D. Noe_, May 02 2013