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A071255 a(1) = 2, a(n+1) = a(n)-th squarefree number > 1.

%I A071255 #23 Aug 05 2025 21:33:12
%S A071255 2,3,5,7,11,17,29,46,74,119,195,319,521,859,1407,2315,3810,6267,10303,
%T A071255 16942,27862,45822,75381,123998,203969,335507,551886,907818,1493294,
%U A071255 2456374,4040526,6646389,10932823,17983831,29582198,48660745,80043762
%N A071255 a(1) = 2, a(n+1) = a(n)-th squarefree number > 1.
%C A071255 Here 1 is not considered a squarefree number.
%H A071255 Daniel Suteu, <a href="/A071255/b071255.txt">Table of n, a(n) for n = 1..90</a>
%F A071255 a(n) = A005117(a(n-1)+1), a(1) = 2.
%F A071255 Limit_{n->infinity} a(n+1)/a(n) = zeta(2). - _Daniel Suteu_, Jul 07 2022
%e A071255 a(2) = 3 and the third squarefree number is 5 hence a(3) = 5.
%e A071255 a(4) = 7 hence a(5) = 11 is the 7th squarefree number (2,3,5,6,7,10,11...)
%e A071255 75381 is the 45822nd squarefree number.
%t A071255 sqf = {}; Do[ If[ SquareFreeQ[n], sqf = Append[sqf, n]], {n, 2, 334000} ]; a[1] = 2; a[n_] := sqf[[ a[n - 1]]]; Table[ a[n], {n, 1, 26}]
%t A071255 a[1]=2; a[x_] := Part[t, a[x-1]] t=Flatten[Position[Table[Abs[MoebiusMu[w]], {w, 2, 35000}], 1]]+1; t1=Table[a[w], {w, 1, 21}]
%Y A071255 Cf. A005117, A013661.
%K A071255 nonn
%O A071255 1,1
%A A071255 _Amarnath Murthy_, May 22 2002
%E A071255 More terms from _Robert G. Wilson v_ and _Labos Elemer_, Jun 07 2002
%E A071255 a(27)-a(37) from _Donovan Johnson_, Oct 29 2010