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Group the natural numbers so that the n-th group contains the smallest still-available set of n numbers whose product is a square.
11

%I #12 Mar 02 2015 02:55:26

%S 1,2,8,3,4,12,5,6,7,210,9,10,11,13,1430,14,15,16,17,18,1785,19,20,21,

%T 22,23,24,168245,25,26,27,28,29,30,31,409045,32,33,34,35,36,37,38,39,

%U 119629510,40,41,42,43,44,45,46,47,48,293493662,49,50,51,52

%N Group the natural numbers so that the n-th group contains the smallest still-available set of n numbers whose product is a square.

%C There is some ambiguity in the definition. Exactly how is the next term to be chosen? Compare A076596, A076696. - _N. J. A. Sloane_, May 20 2003

%e 1;

%e 2, 8;

%e 3, 4, 12;

%e 5, 6, 7, 210;

%e 9, 10, 11, 13, 1430;

%e 14, 15, 16, 17, 18, 1785;

%e ...

%Y Cf. A076027, A076028, A076029, A076030.

%K nonn,tabl

%O 1,2

%A _Amarnath Murthy_, Oct 01 2002

%E Corrected and extended by _Hans Havermann_, Nov 09 2002