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%I #4 Mar 30 2012 18:51:39
%S 1,345,1562505,184783370001360,180972102858416484216240,
%T 221277040503926652746669502425642824
%N Larger of two numbers in lowest terms whose sum, sum of squares and sum of cubes are all squares.
%C To be in lowest terms the two numbers do not need to be coprime, but their highest common factor does need to be squarefree.
%H Andrew Bremner, <a href="http://www.umass.edu/reports/temp77.html">"A Diophantine system"</a>, International Journal of Mathematics and Mathematical Sciences, vol. 9, no. 2, pp. 413-415, 1986. doi:10.1155/S0161171286000522
%H <a href="http://www.kaynet.or.jp/~kay/misc/gentlemandiary.html">Gentleman's Diary Problem</a> (in Japanese)
%H <a href="http://mathforum.org/kb/thread.jspa?forumID=13&threadID=1709558&messageID=6131410#reply-tree">sci.math discussion</a> March 2008
%e a(1)=345 since 184 and 345 have the properties 184+345=529=23^2, 184^2+345^2=152881=391^2 and 184^3+345^3=47293129=6877^2.
%Y Cf. A139265.
%K nonn
%O 0,2
%A _Henry Bottomley_, Apr 13 2008
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