A131134 - OEIS

%I #19 Nov 26 2015 17:08:51

%S 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 88,29,2,16,47,79,112,73,108,4,41,79,118,79,120,27,70,57,34,40,87,45,

%U 94,72,41,93,146,100,31,87,48,53,112,43,104,83,146,105,34,50,117,185,254

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

%H Harvey P. Dale, <a href="/A131134/b131134.txt">Table of n, a(n) for n = 1..1000</a>

%F For n > 1: a(n) = (n + a(n-1)) / GCD(n, a(n-1)). - _Reinhard Zumkeller_, Nov 26 2015

%p 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 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 (Haskell)

%o a131134 n = a131134_list !! (n-1)

%o a131134_list = 1 : zipWith (\v w -> (v+w) `div` gcd v w) [2..] a131134_list

%o -- _Reinhard Zumkeller_, Nov 26 2015

%Y Cf. A131133.

%Y Equals T(n+1,2) for the Adams-Watters triangle, A125605. - _Gerry Myerson_, Mar 18 2010

%K nonn

%O 1,2

%A _Leroy Quet_, Jun 17 2007

%E More terms from _R. J. Mathar_, Oct 17 2007