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

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, 21, 21, 23, 23, 23, 23, 23, 23, 29, 29, 29, 31, 31, 33, 33, 33, 35, 35, 35, 37, 37, 39, 39, 41, 41, 41, 43, 43, 43, 43, 43, 47, 47, 47, 47, 51, 51, 51, 53, 53, 53, 55, 55, 55, 57, 57, 59

Offset

1,5

Comments

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

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Squarefree.

Index entries for sequences related to GCD's.

Formula

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

Mathematica

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 *)

Prog

(PARI) mygcd(x, y) = if (x==y, 1, gcd(x, y));
sqf(n) = {my(v = List(), k=1); until (#v == n, if (issquarefree(k), listput(v, k)); k++); v; }
a(n) = vecmax(setbinop(mygcd, Vec(sqf(n)))); \\ Michel Marcus, Feb 13 2021

Crossrefs

Cf. A005117, A123314.

Sequence in context: A196386 A035158 A196172 * A131507 A203998 A257371

Adjacent sequences: A123310 A123311 A123312 * A123314 A123315 A123316

Keyword

nonn

Author

Reinhard Zumkeller, Sep 25 2006

Extensions

Name corrected by Amiram Eldar, Feb 13 2021

Status

approved