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%I #13 Mar 02 2019 20:52:22
%S 1,2,4,6,9,12,15,19,24,29,35,42,50,58,67,77,88,99,110,122,135,148,161,
%T 175,189,203,218,234,250,266,283,301,320,339,359,380,401,423,445,468,
%U 491,515,540,565,591,618,646,675,704,733,763,794,826,859,893,928,963
%N a(1)=1; a(n) = a(n-1) + (number of terms, from among terms a(1) through a(n-1), which are squarefree).
%H Harvey P. Dale, <a href="/A130025/b130025.txt">Table of n, a(n) for n = 1..1000</a>
%e Among the first 8 terms of the sequence there are 5 squarefree integers (1,2,6,15,19). So a(9) = a(8) + 5 = 24.
%p with(numtheory): a[1] := 1: for n from 2 to 60 do ct := 0: for j to n-1 do if abs(mobius(a[j])) > 0 then ct := ct+1 else ct := ct end if end do: a[n] := a[n-1]+ct end do: seq(a[n], n = 1 .. 60); # _Emeric Deutsch_, Jul 18 2007
%t nxt[{t_,a_}]:={If[SquareFreeQ[t+a],1,0]+t,t+a}; Transpose[NestList[nxt,{1,1},60]][[2]] (* _Harvey P. Dale_, Jan 04 2015 *)
%K nonn
%O 1,2
%A _Leroy Quet_, Jun 20 2007
%E More terms from _Emeric Deutsch_ and _Joshua Zucker_, Jul 18 2007
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