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A120090
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Numbers whose square is the perimeter of a primitive Pythagorean triangle.
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2
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12, 30, 56, 90, 132, 154, 182, 208, 234, 240, 306, 340, 374, 380, 408, 418, 456, 462, 494, 546, 552, 598, 644, 650, 690, 700, 736, 756, 800, 850, 864, 870, 918, 928, 986, 992, 1026, 1044, 1054, 1102, 1116, 1122, 1160, 1178, 1240, 1254, 1260, 1302, 1320
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(n)=sqrt(A120089).
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LINKS
| P. Yiu, "Primitive Pythagorean triangles with square perimeters" in 'Recreational Mathematics' Chap.6.2 pp. 50/360
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FORMULA
| a(n)=2*u*v, where u=sqrt(j/2) and v=sqrt(j+k) {for coprime pairs(j,k) j>k with odd k such that pairs (u,v) are coprime with v odd}.
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MAPLE
| isA024364 := proc(an) local r::integer, s::integer ; for r from floor((an/4)^(1/2)) to floor((an/2)^(1/2)) do for s from r-1 to 1 by -2 do if 2*r*(r+s) = an and gcd(r, s) < 2 then RETURN(true) ; fi ; if 2*r*(r+s) < an then break ; fi ; od ; od : RETURN(false) ; end : for n from 2 to 1200 do if isA024364(n^2) then printf("%d, ", n) ; fi ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 08 2006
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CROSSREFS
| Sequence in context: A131874 A111396 A080385 * A086830 A084699 A064483
Adjacent sequences: A120087 A120088 A120089 * A120091 A120092 A120093
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KEYWORD
| nonn
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AUTHOR
| Lekraj Beedassy (blekraj(AT)yahoo.com), Jun 07 2006
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EXTENSIONS
| Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 08 2006
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