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%I #15 Mar 02 2019 23:32:20
%S 1,1,2,3,5,8,13,15,28,43,57,100,157,167,324,491,497,988,1485,1979,
%T 2144,4123,4257,8380,9799,13989,23788,37777,49671,87448,104005,125867,
%U 229872,355739,384473,740212,1124685,1494791,1536446,3031237,4567683,7598920
%N a(1) = a(2) = 1, a(n) = a(n-1) + A007947(a(n-2)) for n >= 3, i.e., a(n) = a(n-1) plus the largest squarefree divisor of a(n-2).
%e 14 is the largest squarefree divisor of a(9) = 28. So a(11) = a(10) + 14 = 57.
%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 a(n-1)+A007947(a(n-2)) fi end: seq(a(n),n=1..20); # _Emeric Deutsch_, Jul 24 2006
%t nxt[{a_,b_}]:={b,b+Max[Select[Divisors[a],SquareFreeQ]]}; Transpose[ NestList[ nxt,{1,1},50]][[1]] (* _Harvey P. Dale_, Jul 23 2015 *)
%Y Cf. A007947, A121368, 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 11 2007
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