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A123313 Maximum of greatest common divisors of pairs of distinct squarefree numbers not greater than the n-th squarefree number; a(1)=1.

%I A123313 #23 Feb 16 2025 08:33:02
%S A123313 1,1,1,1,3,3,5,5,5,7,7,7,7,7,11,11,13,13,15,15,15,17,17,17,19,19,19,
%T A123313 21,21,23,23,23,23,23,23,29,29,29,31,31,33,33,33,35,35,35,37,37,39,39,
%U A123313 41,41,41,43,43,43,43,43,47,47,47,47,51,51,51,53,53,53,55,55,55,57,57,59
%N A123313 Maximum of greatest common divisors of pairs of distinct squarefree numbers not greater than the n-th squarefree number; a(1)=1.
%C A123313 A123314(n) = #{k: a(k) = A005117(n)}.
%H A123313 Reinhard Zumkeller, <a href="/A123313/b123313.txt">Table of n, a(n) for n = 1..10000</a>
%H A123313 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Squarefree.html">Squarefree</a>.
%H A123313 <a href="/index/Ga#gcd">Index entries for sequences related to GCD's</a>.
%F A123313 a(n) = Max(a(n-1), Max(GCD(A005117(n), A005117(k)): 1<=k<n)).
%t A123313 seq[max_] := Module[{sqf = Select[Range[max], SquareFreeQ], s, m}, m = Length[sqf]; s = Table[0, {m}]; s[[1]] = 1; Do[s[[k]] = Max[s[[k - 1]], Max[GCD[sqf[[k]], Take[sqf, k - 1]]]], {k, 2, m}]; s]; seq[120] (* _Amiram Eldar_, Feb 13 2021 *)
%o A123313 (PARI) mygcd(x, y) = if (x==y, 1, gcd(x,y));
%o A123313 sqf(n) = {my(v = List(), k=1); until (#v == n, if (issquarefree(k), listput(v, k)); k++); v;}
%o A123313 a(n) = vecmax(setbinop(mygcd, Vec(sqf(n)))); \\ _Michel Marcus_, Feb 13 2021
%Y A123313 Cf. A005117, A123314.
%K A123313 nonn
%O A123313 1,5
%A A123313 _Reinhard Zumkeller_, Sep 25 2006
%E A123313 Name corrected by _Amiram Eldar_, Feb 13 2021