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%I #15 Jul 21 2017 13:33:50
%S 1,1,2,3,5,8,7,15,22,37,59,96,65,161,226,387,355,742,1097,1839,2936,
%T 2573,5509,8082,8203,16285,24488,22407,46895,69302,116197,185499,
%U 178030,363529,541559,905088,555701,1460789,591330,2052119,2643449,4695568
%N a(1) = a(2) = 1, a(n) = A007947(a(n-1)) + a(n-2), for n >= 3, i.e., a(n) = a(n-2) plus the largest squarefree divisor of a(n-1).
%H Harvey P. Dale, <a href="/A121368/b121368.txt">Table of n, a(n) for n = 1..200</a>
%e 6 is the largest squarefree divisor of a(12) = 96. So a(13) = 6 + a(11) = 65.
%p 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))+a(n-2) fi end: seq(a(n),n=1..25); # _Emeric Deutsch_, Jul 24 2006
%t nxt[{a_,b_}]:={b,a+Max[Select[Divisors[b],SquareFreeQ]]}; NestList[nxt,{1,1},50][[All,1]] (* _Harvey P. Dale_, Jan 21 2017 *)
%Y Cf. A007947, A121367, A121369.
%K nonn
%O 1,3
%A _Leroy Quet_, Jul 23 2006
%E More terms from _Emeric Deutsch_, Jul 24 2006
%E More terms from _R. J. Mathar_, May 18 2007
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