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A120090 Numbers whose square is the perimeter of a primitive Pythagorean triangle. 2
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; text; internal format)
OFFSET

1,1

COMMENTS

a(n) = sqrt(A120089).

LINKS

Table of n, a(n) for n=1..49.

P. Yiu, "Primitive Pythagorean triangles with square perimeters" in 'Recreational Mathematics' Chap. 6.2 pp. 50/360

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}.

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, Jun 08 2006

CROSSREFS

Sequence in context: A131874 A111396 A080385 * A280344 A286497 A086830

Adjacent sequences:  A120087 A120088 A120089 * A120091 A120092 A120093

KEYWORD

nonn

AUTHOR

Lekraj Beedassy, Jun 07 2006

EXTENSIONS

Corrected and extended by R. J. Mathar, Jun 08 2006

STATUS

approved

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Last modified September 26 01:25 EDT 2017. Contains 292500 sequences.