A146984 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, ...).

5, 5, 13, 10, 25, 17, 41, 10, 15, 26, 61, 37, 85, 20, 50, 113, 15, 39, 65, 145, 13, 25, 34, 82, 181, 101, 221, 17, 20, 30, 52, 75, 122, 265, 145, 313, 29, 35, 74, 170, 365, 25, 29, 51, 65, 123, 197, 421, 40, 100, 226, 481, 257, 545, 30, 45, 53, 78, 130, 183

Offset: 1

Author

Pahikkala Jussi, Nov 04 2008

Keywords

• easy
• nonn

Comments

Any number a(n) is also a hypotenuse number A009003 (and conversely) - see Pahikkala 2010, Theorem 5.

Examples

			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.
		

Links

• Jussi Pahikkala, On contraharmonic mean and Pythagorean triples, Elemente der Mathematik, 65:2 (2010), 62-67.
• PlanetMath, Contraharmonic proportion
• PlanetMath, Integer contraharmonic means [From _Pahikkala Jussi_, Sep 05 2010]

Crossrefs

After sorting and removing duplicates we get A009003. - N. J. A. Sloane, Mar 20 2011

Programs

Maple

K:=100; t1:=[];
for u from 1 to K-1 do for v from u+1 to 2*u^2-u do
if (u^2+v^2) mod (u+v) = 0 then t1:=[op(t1),(u^2+v^2)/(u+v)]; fi;
od: od: t1; # N. J. A. Sloane, Mar 20 2011

Formula

The contraharmonic mean of u and v is (u^2+v^2)/(u+v).

Extensions

Minor edits by N. J. A. Sloane, Mar 20 2011