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%I #31 Aug 16 2020 10:41:45
%S 5,5,13,10,25,17,41,10,15,26,61,37,85,20,50,113,15,39,65,145,13,25,34,
%T 82,181,101,221,17,20,30,52,75,122,265,145,313,29,35,74,170,365,25,29,
%U 51,65,123,197,421,40,100,226,481,257,545,30,45,53,78,130,183
%N List of integer-valued contraharmonic means (u^2+v^2)/(u+v) of two positive integers u and v (with u < v) ordered by increasing u and increasing v (u = 2, 3, 4, ...; v = u+1, u+2, ...).
%C Any number a(n) is also a hypotenuse number A009003 (and conversely) - see Pahikkala 2010, Theorem 5.
%H Jussi Pahikkala, <a href="https://doi.org/10.4171/EM/141">On contraharmonic mean and Pythagorean triples</a>, Elemente der Mathematik, 65:2 (2010), 62-67.
%H PlanetMath, <a href="http://planetmath.org/ContraharmonicProportion">Contraharmonic proportion</a>
%H PlanetMath, <a href="http://planetmath.org/IntegerContraharmonicMeans">Integer contraharmonic means</a> [From _Pahikkala Jussi_, Sep 05 2010]
%F The contraharmonic mean of u and v is (u^2+v^2)/(u+v).
%e a(1) = (2^2+6^2)/(2+6) = 5, a(2) = (3^2+6^2)/(3+6) = 5, a(3) = (3^2+15^2)/(3+15) = 13.
%p K:=100; t1:=[];
%p for u from 1 to K-1 do for v from u+1 to 2*u^2-u do
%p if (u^2+v^2) mod (u+v) = 0 then t1:=[op(t1),(u^2+v^2)/(u+v)]; fi;
%p od: od: t1; # _N. J. A. Sloane_, Mar 20 2011
%Y After sorting and removing duplicates we get A009003. - _N. J. A. Sloane_, Mar 20 2011
%K easy,nonn
%O 1,1
%A _Pahikkala Jussi_, Nov 04 2008
%E Minor edits by _N. J. A. Sloane_, Mar 20 2011
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