Search: id:A156688
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%I A156688
%S A156688 2,3,6,4,6,9,6,5,10,9,6,12,6,9,18,6,6,15,6,12,18,9,6,15,10,9,14,12,6,27,
%T A156688 6,7,18,9,18,20,6,9,18,15,6,27,6,12,30,9,6,18,10,15,18,12,6,21,18,15,18,
%U A156688 9,6,36,6,9,30,8,18,27,6,12,18,27,6,25,6,9,30
%N A156688 The total number of distinct Pythagorean triples with an area numerically 
               equal to n times their perimeters
%C A156688 The members of this sequence are also 1/2 the number of divisors of 8n^2. 
               The corresponding results for primitive triangles only are in A068068.
%D A156688 Chi, Henjin and Killgrove, Raymond; Problem 1447, Crux Math 15(5), May 
               1989.
%D A156688 Chi, Henjin and Killgrove, Raymond; Solution to Problem 1447, Crux Math 
               16(7), September 1990.
%H A156688 Ron Knott, <a href="http://www.mcs.surrey.ac.uk/Personal/R.Knott/Pythag/
               pythag.html">Right-angled Triangles and Pythagoras' Theorem</a>
%F A156688 1/2 d(8n^2)=1/2 A000005(8n^2)
%e A156688 There are 6 Pythagorean triples whose area is 5 times their perimeters 
               - (21,220,221), (22,120,122), (24,70,74), (25,60,65),(28,45,53) and 
               (30,40,50) - hence a(5)=6.
%t A156688 1/2 DivisorSigma[0,8#^2] &/@Range[75]
%Y A156688 A000005, A068068
%Y A156688 Sequence in context: A127915 A072637 A125703 this_sequence A019567 A098286 
               A138608
%Y A156688 Adjacent sequences: A156685 A156686 A156687 this_sequence A156689 A156690 
               A156691
%K A156688 easy,nice,nonn
%O A156688 1,1
%A A156688 Ant King (mathstutoring(AT)ntlworld.com), Feb 18 2009

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