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A121369 a(1) = a(2) = 1, a(n) = A007947(a(n-1)) + A007947(a(n-2)) for n >= 3, i.e., a(n) is the largest squarefree divisor of a(n-1) plus the largest squarefree divisor of a(n-2).

%I A121369 #23 Jan 08 2018 02:37:06
%S A121369 1,1,2,3,5,8,7,9,10,13,23,36,29,35,64,37,39,76,77,115,192,121,17,28,
%T A121369 31,45,46,61,107,168,149,191,340,361,189,40,31,41,72,47,53,100,63,31,
%U A121369 52,57,83,140,153,121,62,73,135,88,37,59,96,65,71,136,105,139,244,261,209,296
%N A121369 a(1) = a(2) = 1, a(n) = A007947(a(n-1)) + A007947(a(n-2)) for n >= 3, i.e., a(n) is the largest squarefree divisor of a(n-1) plus the largest squarefree divisor of a(n-2).
%C A121369 First terms occurring more than once: 1, 31, 37, 121, ...: a(25)=a(37)=a(44)=31, a(16)=a(55)=37, a(22)=a(50)=121. - _Reinhard Zumkeller_, May 05 2013
%H A121369 Reinhard Zumkeller and Michael De Vlieger, <a href="/A121369/b121369.txt">Table of n, a(n) for n = 1..1000</a> (first 250 terms from Reinhard Zumkeller).
%e A121369 6 is the largest squarefree divisor of a(12) = 36. 29 is the largest squarefree divisor of a(13) = 29. So a(14) = 6 + 29 = 35.
%p A121369 with(numtheory): A007947:= proc(n) local i, t1, t2; t1 := ifactors(n)[2]; t2 := mul(t1[i][1], i=1..nops(t1)); end: a:=proc(n) if n=1 or n=2 then 1 else A007947(a(n-1))+A007947(a(n-2)) fi end: seq(a(n),n=1..20); # _Emeric Deutsch_, Jul 24 2006
%t A121369 Nest[Append[#, Total@ Map[SelectFirst[Reverse@ Divisors@ #, SquareFreeQ] &, Take[#, -2]]] &, {1, 1}, 64] (* _Michael De Vlieger_, Oct 10 2017 *)
%o A121369 (Haskell)
%o A121369 import Data.Function (on)
%o A121369 a121369 n = a121369_list !! (n-1)
%o A121369 a121369_list = 1 : 1 : zipWith ((+) `on` a007947)
%o A121369                        a121369_list (tail a121369_list)
%o A121369 -- _Reinhard Zumkeller_, May 05 2013
%Y A121369 Cf. A007947, A121367, A121368.
%Y A121369 Cf. A000045.
%K A121369 nonn
%O A121369 1,3
%A A121369 _Leroy Quet_, Jul 23 2006
%E A121369 More terms from _Emeric Deutsch_, Jul 24 2006
%E A121369 More terms from _R. J. Mathar_, May 18 2007