A123313 - OEIS

%I #18 Feb 13 2021 14:38:02

%S 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 21,21,23,23,23,23,23,23,29,29,29,31,31,33,33,33,35,35,35,37,37,39,39,

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

%C A123314(n) = #{k: a(k) = A005117(n)}.

%H Reinhard Zumkeller, <a href="/A123313/b123313.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Squarefree.html">Squarefree</a>.

%H <a href="/index/Ga#gcd">Index entries for sequences related to GCD's</a>.

%F a(n) = Max(a(n-1), Max(GCD(A005117(n), A005117(k)): 1<=k<n).

%t 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 (PARI) mygcd(x, y) = if (x==y, 1, gcd(x,y));

%o sqf(n) = {my(v = List(), k=1); until (#v == n, if (issquarefree(k), listput(v, k)); k++); v;}

%o a(n) = vecmax(setbinop(mygcd, Vec(sqf(n)))); \\ _Michel Marcus_, Feb 13 2021

%Y Cf. A005117, A123314.

%K nonn

%O 1,5

%A _Reinhard Zumkeller_, Sep 25 2006

%E Name corrected by _Amiram Eldar_, Feb 13 2021