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A120089
Square perimeters of primitive Pythagorean triangles.
2
144, 900, 3136, 8100, 17424, 23716, 33124, 43264, 54756, 57600, 93636, 115600, 139876, 144400, 166464, 174724, 207936, 213444, 244036, 298116, 304704, 357604, 414736, 422500, 476100, 490000, 541696, 571536, 640000, 722500, 746496, 756900
OFFSET
1,1
COMMENTS
Square entries of A024364.
FORMULA
a(n) = (2*u*v)^2, 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),u<v are coprime with v odd}.
a(n) = A024364(k) = A000290(j) for some k and j. - R. J. Mathar, Jun 08 2006
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 : isA120089 := proc(an) RETURN( issqr(an) and isA024364(an)) ; end: for n from 2 to 1200 do if isA120089(n^2) then printf("%d, ", n^2) ; fi ; od ; # R. J. Mathar, Jun 08 2006
MATHEMATICA
A078926[n_] := Sum[Boole[n < d^2 < 2n && CoprimeQ[d, n/d]], {d, Divisors[n/2^IntegerExponent[n, 2]]}];
Reap[For[k = 2, k <= 10^6, k += 2, If[A078926[k/2] > 0 && IntegerQ@Sqrt@k, Print[k]; Sow[k]]]][[2, 1]] (* Jean-François Alcover, Oct 25 2023 *)
CROSSREFS
Cf. A120090.
Sequence in context: A234084 A223235 A187301 * A159748 A235957 A162669
KEYWORD
nonn
AUTHOR
Lekraj Beedassy, Jun 07 2006
EXTENSIONS
Corrected and extended by R. J. Mathar, Jun 08 2006
STATUS
approved