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 A135507 #28 May 20 2024 14:08:14
%S A135507 1,4,20,60,180,540,4860,19440,58320,174960,2274480,6823440,20470320,
%T A135507 184232880,552698640,1658095920,31503822480,94511467440,283534402320,
%U A135507 850603206960,7655428862640,99520575214320,2488014380358000
%N A135507 a(1) = 1; for n > 1, a(n) = 2*a(n-1) + lcm(a(n-1),n).
%C A135507 This sequence has properties related to primes and especially to twin primes. For instance a(n+1)/a(n)-2 is never the largest prime of a twin pair (except for 7).
%C A135507 Conjecture: Let p = a(n+1)/a(n)-2. If p is prime then p = A140460(m) or p = A140460(m) + 2 for some m. - _Bill McEachen_, Apr 04 2024
%H A135507 Reinhard Zumkeller, <a href="/A135507/b135507.txt">Table of n, a(n) for n = 1..1000</a>
%t A135507 a[1] = 1; a[n_] := a[n] = 2*a[n-1] + LCM[a[n-1], n]; Table[a[n], {n, 1, 23}] (* _Jean-François Alcover_, Dec 06 2012 *)
%t A135507 nxt[{n_,a_}]:={n+1,2a+LCM[a,n+1]}; Transpose[NestList[nxt,{1,1},30]][[2]] (* _Harvey P. Dale_, Oct 16 2014 *)
%o A135507 (PARI) x1=1;for(n=2,40,x2=2*x1+lcm(x1,n);t=x1;x1=x2;print1(x2,","))
%o A135507 (Haskell)
%o A135507 a135507 n = a135507_list !! (n-1)
%o A135507 a135507_list = 1 : zipWith (+)
%o A135507 (map (* 2) $ a135507_list) (zipWith lcm a135507_list [2..])
%o A135507 -- _Reinhard Zumkeller_, Mar 25 2012
%Y A135507 Cf. A106108.
%K A135507 nonn,nice
%O A135507 1,2
%A A135507 _Benoit Cloitre_, Feb 09 2008, Feb 10 2008