Search: id:A083854
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%I A083854
%S A083854 0,1,2,3,4,6,8,9,12,16,18,24,25,27,32,36,48,49,50,54,64,72,75,81,96,98,
%T A083854 100,108,121,128,144,147,150,162,169,192,196,200,216,225,242,243,256,
%U A083854 288,289,294,300,324,338,361,363,384,392,400,432,441,450,484,486,507
%N A083854 Numbers which are squares, twice squares, three times squares, or six 
               times squares: i.e. numbers whose square-free part divides 6.
%C A083854 It is simple to divide equilateral triangles into these numbers of congruent 
               parts: squares by making smaller equilateral triangles; 6*squares 
               by diving each small equilateral triangles by its medians into small 
               right-angled triangles; and 2*squares or 3*squares by recombining 
               three or two of these small right-angled triangles.
%F A083854 a(n) is bounded below by 0.137918...*n^2 where 0.137918...=3*(3-2*sqrt(2))*(2-sqrt(3)); 
               the error appears to be O(n).
%Y A083854 Cf. A000290, A007913, A001105, A028982, A033428, A033581, A083855.
%Y A083854 Sequence in context: A067947 A053640 A097755 this_sequence A003586 A114334 
               A018690
%Y A083854 Adjacent sequences: A083851 A083852 A083853 this_sequence A083855 A083856 
               A083857
%K A083854 nonn
%O A083854 0,3
%A A083854 Henry Bottomley (se16(AT)btinternet.com), May 06 2003

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