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 A083538 #17 Mar 15 2018 04:11:32
%S A083538 3,12,28,42,2,6,120,195,234,6,21,2,84,1,744,558,78,780,210,336,72,6,
%T A083538 10,1860,1302,420,35,420,60,36,2016,336,72,72,4368,3458,570,210,1260,
%U A083538 105,112,264,231,182,156,6,372,7068,589,744,1764,1323,180,15,15,6,72,6,70
%N A083538 a(n) = sigma(n)*sigma(n+1)/gcd(sigma(n+1), sigma(n))^2.
%C A083538 a(n) = A060781(n)/A060780(n) = A083539(n)/A060780(n)^2; quotient when lcm(sigma(n+1), sigma(n)) is divided by gcd(sigma(n+1), sigma(n)).
%H A083538 Charles R Greathouse IV, <a href="/A083538/b083538.txt">Table of n, a(n) for n = 1..10000</a>
%e A083538 n=10: sigma(10)=18, sigma(11)=12, lcm(18, 12)=36, gcd(18, 12)=6, a(10) = 36/6 = 6.
%t A083538 f[x_] := DivisorSigma[1, x] t=Table[LCM[f[w+1], f[w]]/GCD[f[w+1], f[w]], {w, 1, 128}]
%t A083538 Times@@#/(GCD@@#)^2&/@Partition[DivisorSigma[1,Range[60]],2,1] (* _Harvey P. Dale_, Feb 17 2016 *)
%o A083538 (PARI) a(n)=my(x=sigma(n),y=sigma(n+1)); x*y/gcd(x,y)^2 \\ _Charles R Greathouse IV_, Mar 09 2014
%Y A083538 Cf. A000010, A066813, A058515, A000203, A060781, A060780, A083539.
%K A083538 nonn
%O A083538 1,1
%A A083538 _Labos Elemer_, May 21 2003
%E A083538 Edited by _N. J. A. Sloane_, Apr 29 2007
%E A083538 Corrections by _Charles R Greathouse IV_, Mar 09 2014