cp's OEIS Frontend

A214799 Let S be a set of n positive numbers such that all n choose 2 pairwise GCD's are distinct, and let max(S) denote the largest element of S; a(n) is the minimal value of max(S) over all choices for S.

%I A214799 #25 Mar 07 2013 16:06:05
%S A214799 1,2,6,18,54,120,240,480,960,1920
%N A214799 Let S be a set of n positive numbers such that all n choose 2 pairwise GCD's are distinct, and let max(S) denote the largest element of S; a(n) is the minimal value of max(S) over all choices for S.
%F A214799 Conjecture: a(n) = 15 * 2^(n-3) for n >= 6 (_Robert Israel_)
%e A214799 n   a(n)      Example of S
%e A214799 ---------------------------
%e A214799 1    1       {1}
%e A214799 2    2       {1,2}
%e A214799 3    6       {2,3,6}
%e A214799 4   18       {4,9,12,18}
%e A214799 5   54       {8,24,27,36,54}
%e A214799 6  120       {45,80,84,90,112,120}
%e A214799 7  240       {45,126,160,168,180,224,240}
%e A214799 8  480       {135,252,270,320,336,360,448,480}
%e A214799 9  960       {504, 640, 672, 720, 756, 810, 896, 945, 960}
%e A214799 10 1920      {1008, 1215, 1280, 1344, 1440, 1512, 1620, 1792, 1890, 1920}
%Y A214799 Cf. A061799 (minimum of smallest element), A213918.
%K A214799 nonn
%O A214799 1,2
%A A214799 _N. J. A. Sloane_, Mar 07 2013
%E A214799 a(4)-a(8) from _Robert Israel_, Mar 05 2013.
%E A214799 a(9)-a(10) from _Giovanni Resta_, Mar 06 2013