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a(0)=a(1)=1. a(n) = gcd(a(n-1), n) + gcd(a(n-2), n).
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%I #22 May 15 2019 04:53:18

%S 1,1,2,2,4,2,4,2,6,4,4,2,6,2,4,2,6,2,8,2,6,4,4,2,6,2,4,2,6,2,8,2,10,2,

%T 4,2,6,2,4,2,6,2,8,2,6,4,4,2,6,2,4,2,6,2,8,2,10,2,4,2,6,2,4,2,6,2,8,2,

%U 6,4,4,2,6,2,4,2,6,2,8,2,10,2,4,2,6,2,4,2,6,2,8,2,6,4,4,2,6,2,4,2,6,2,8,2

%N a(0)=a(1)=1. a(n) = gcd(a(n-1), n) + gcd(a(n-2), n).

%C a(n) is even for all n >= 2.

%H Harvey P. Dale, <a href="/A129089/b129089.txt">Table of n, a(n) for n = 0..1000</a>

%p a[0]:=1: a[1]:=1: for n from 2 to 130 do a[n]:=igcd(a[n-1],n)+igcd(a[n-2],n) od: seq(a[n],n=0..130); # _Emeric Deutsch_, Apr 16 2007

%t nxt[{n_,a_,b_}]:={n+1,b,GCD[b,n+1]+GCD[a,n+1]}; Join[{1},NestList[nxt,{1,1,1},110][[All,3]]] (* _Harvey P. Dale_, May 23 2017 *)

%Y Cf. A129088.

%K nonn

%O 0,3

%A _Leroy Quet_, Mar 29 2007

%E More terms from _Emeric Deutsch_, Apr 16 2007

%E Incorrect g.f. removed by _Georg Fischer_, May 15 2019