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%I #19 Oct 16 2014 15:25:59
%S 1,4,20,60,180,540,4860,19440,58320,174960,2274480,6823440,20470320,
%T 184232880,552698640,1658095920,31503822480,94511467440,283534402320,
%U 850603206960,7655428862640,99520575214320,2488014380358000
%N a(1)=1; for n>1, a(n)=2*a(n-1)+lcm(a(n-1),n).
%C 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).
%H Reinhard Zumkeller, <a href="/A135507/b135507.txt">Table of n, a(n) for n = 1..1000</a>
%t 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 nxt[{n_,a_}]:={n+1,2a+LCM[a,n+1]}; Transpose[NestList[nxt,{1,1},30]][[2]] (* _Harvey P. Dale_, Oct 16 2014 *)
%o (PARI) x1=1;for(n=2,40,x2=2*x1+lcm(x1,n);t=x1;x1=x2;print1(x2,","))
%o (Haskell)
%o a135507 n = a135507_list !! (n-1)
%o a135507_list = 1 : zipWith (+)
%o (map (* 2) $ a135507_list) (zipWith lcm a135507_list [2..])
%o -- _Reinhard Zumkeller_, Mar 25 2012
%Y Cf. A106108.
%K nonn,nice
%O 1,2
%A _Benoit Cloitre_, Feb 09 2008, Feb 10 2008
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