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 A083531 #21 Mar 08 2024 08:28:07
%S A083531 2,1,2,1,1,4,1,1,1,3,2,4,4,2,1,1,4,2,1,1,2,2,4,6,2,1,3,2,1,5,4,2,4,2,
%T A083531 4,6,1,2,3,2,4,2,4,2,2,2,6,1,3,2,1,1,4,1,5,2,4,6,2,4,2,2,2,2,4,3,3,2,
%U A083531 4,2,1,3,6,2,1,3,2,4,6,2,4,1,5,2,4,2,4,6,2,6,4,3,1,2,2,4,2,4,2,6,2,2,2,4,6
%N A083531 First difference sequence of A002191. Differences between possible values for sum of divisors of n.
%H A083531 Michael De Vlieger, <a href="/A083531/b083531.txt">Table of n, a(n) for n = 1..10000</a>
%e A083531 8 and 12 are the 6th and 7th possible values for sigma(x), since they are sum of divisors of x = 7 and x = 11 respectively, while 9, 10, 11 are impossible ones so 12 - 8 = 4 = a(6) = A002191(7) - A002191(6).
%e A083531 From _Michael De Vlieger_, Jul 22 2017: (Start)
%e A083531 First position of values:
%e A083531 Value First position
%e A083531 1 2
%e A083531 2 1
%e A083531 3 10
%e A083531 4 6
%e A083531 5 30
%e A083531 6 24
%e A083531 7 277
%e A083531 8 165
%e A083531 9 509
%e A083531 10 150
%e A083531 11 824
%e A083531 12 400
%e A083531 13 10970
%e A083531 14 1400
%e A083531 15 10448
%e A083531 16 1182
%e A083531 17 18731
%e A083531 18 2218
%e A083531 19 209237
%e A083531 20 3420
%e A083531 21 127385
%e A083531 22 6910
%e A083531 23 28899
%e A083531 24 5377
%e A083531 (End)
%t A083531 t=Table[DivisorSigma[1, w], {w, 1, 25000}]; u=Union[%]; Delete[u-RotateRight[u], 1]
%t A083531 (* Second program: *)
%t A083531 With[{nn = 300}, Differences@ TakeWhile[Union@ DivisorSigma[1, Range@ nn], # < nn &]] (* _Michael De Vlieger_, Jul 22 2017 *)
%Y A083531 Cf. A002191, A007609, A007369, A083532, A083533, A083534, A083535, A083536, A109323 (start of record gaps in A002191).
%K A083531 nonn
%O A083531 1,1
%A A083531 _Labos Elemer_, May 20 2003