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 A083540 #14 Apr 09 2021 03:51:00
%S A083540 14,30,51,161,186,206,223,329,552,713,759,869,957,994,995,1248,1334,
%T A083540 1364,1634,1715,1819,2093,2133,2584,2685,2820,2821,2974,3115,3145,
%U A083540 3485,4212,4308,4312,4364,4408,4649
%N A083540 Numbers k such that A083539(k) is a square; solutions x to sigma(x+1)*sigma(x)=y^2 for some y.
%H A083540 Amiram Eldar, <a href="/A083540/b083540.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%e A083540 x=30: sigma(30)=72, sigma(31)=32, product = 72*32 = 256*9 = 24^2.
%t A083540 Do[s=Sqrt[DivisorSigma[1, n+1]*DivisorSigma[1, n]]; If[IntegerQ[s], Print[n]], {n, 1, 5000}]
%t A083540 Flatten[Position[Times@@@Partition[DivisorSigma[1,Range[5000]],2,1], _?(IntegerQ[Sqrt[#]]&)]] (* _Harvey P. Dale_, Mar 07 2016 *)
%Y A083540 Cf. A000203, A083539, A060780, A060781, A083538.
%K A083540 nonn
%O A083540 1,1
%A A083540 _Labos Elemer_, May 21 2003