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.

1, 2, 6, 18, 54, 120, 240, 480, 960, 1920

Offset: 1

Author

N. J. A. Sloane, Mar 07 2013

Keywords

• nonn

Examples

			n   a(n)      Example of S
---------------------------
1    1       {1}
2    2       {1,2}
3    6       {2,3,6}
4   18       {4,9,12,18}
5   54       {8,24,27,36,54}
6  120       {45,80,84,90,112,120}
7  240       {45,126,160,168,180,224,240}
8  480       {135,252,270,320,336,360,448,480}
9  960       {504, 640, 672, 720, 756, 810, 896, 945, 960}
10 1920      {1008, 1215, 1280, 1344, 1440, 1512, 1620, 1792, 1890, 1920}
		

Crossrefs

Cf. A061799 (minimum of smallest element), A213918.

Formula

Conjecture: a(n) = 15 * 2^(n-3) for n >= 6 (Robert Israel)

Extensions

a(4)-a(8) from Robert Israel, Mar 05 2013.

a(9)-a(10) from Giovanni Resta, Mar 06 2013