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A146984
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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, ...).
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Any number a(n) is also a hypotenuse number A009003 (and conversely) - see Pahikkala 2010 , Theorem 5.
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REFERENCES
| Pahikkala Jussi, On contraharmonic mean and Pythagorean triples, Elemente der Mathematik, 65:2 (2010), 62-67. [From Pahikkala Jussi (pahio(AT)wakkanet.fi), Sep 05 2010]
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LINKS
| J. Pahikkala, On contraharmonic mean and Pythagorean triples
PlanetMath, Contraharmonic proportion
PlanetMath, Integer contraharmonic means [From Pahikkala Jussi (pahio(AT)wakkanet.fi), Sep 05 2010]
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FORMULA
| The contraharmonic mean of u and v is (u^2+v^2)/(u+v).
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EXAMPLE
| 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.
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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; [From N. J. A. Sloane, Mar 20 2011]
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PROG
| K = 50 (e.g.) FOR u = 2 TO K FOR v = u TO 2u^2-u a := (u^2+v^2)/(u+v) IF INT(a) = a THEN PRINT u, v, a NEXT v NEXT u
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CROSSREFS
| After sorting and removing duplicates we get A009003. - N. J. A. Sloane, Mar 20 2011.
Sequence in context: A122213 A049735 A055526 * A055524 A132981 A168392
Adjacent sequences: A146981 A146982 A146983 * A146985 A146986 A146987
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KEYWORD
| easy,nonn
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AUTHOR
| Pahikkala Jussi (pahio(AT)wakkanet.fi), Nov 04 2008
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EXTENSIONS
| Minor edits by N. J. A. Sloane, Mar 20 2011
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