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A131134 a(1)=1. a(n) = (1/n + 1/a(n-1)) * lcm(n,a(n-1)).

%I A131134 #19 Nov 26 2015 17:08:51
%S A131134 1,3,2,3,8,7,2,5,14,12,23,35,48,31,46,31,48,11,30,5,26,24,47,71,96,61,
%T A131134 88,29,2,16,47,79,112,73,108,4,41,79,118,79,120,27,70,57,34,40,87,45,
%U A131134 94,72,41,93,146,100,31,87,48,53,112,43,104,83,146,105,34,50,117,185,254
%N A131134 a(1)=1. a(n) = (1/n + 1/a(n-1)) * lcm(n,a(n-1)).
%H A131134 Harvey P. Dale, <a href="/A131134/b131134.txt">Table of n, a(n) for n = 1..1000</a>
%F A131134 For n > 1: a(n) = (n + a(n-1)) / GCD(n, a(n-1)). - _Reinhard Zumkeller_, Nov 26 2015
%p A131134 A131134 := proc(n) option remember ; if n = 1 then 1; else (1/n+1/A131134(n-1))*lcm(n,A131134(n-1)) ; fi ; end: seq(A131134(n),n=1..80) ; # _R. J. Mathar_, Oct 17 2007
%t A131134 nxt[{n_,a_}]:={n+1,(1/(n+1)+1/a)LCM[n+1,a]}; Transpose[NestList[nxt,{1,1},70]][[2]] (* _Harvey P. Dale_, Aug 13 2013 *)
%o A131134 (Haskell)
%o A131134 a131134 n = a131134_list !! (n-1)
%o A131134 a131134_list = 1 : zipWith (\v w -> (v+w) `div` gcd v w) [2..] a131134_list
%o A131134 -- _Reinhard Zumkeller_, Nov 26 2015
%Y A131134 Cf. A131133.
%Y A131134 Equals T(n+1,2) for the Adams-Watters triangle, A125605. - _Gerry Myerson_, Mar 18 2010
%K A131134 nonn
%O A131134 1,2
%A A131134 _Leroy Quet_, Jun 17 2007
%E A131134 More terms from _R. J. Mathar_, Oct 17 2007