A120090 -id:A120090 - cp's OEIS frontend

A120091 Ordered values j of pairs (j,k) that generate A120090.

8, 18, 32, 50, 72, 98, 98, 128, 128, 162, 162, 200, 200, 242, 242, 242, 288, 288, 288, 338, 338, 338, 338, 392, 392, 392, 450, 450, 512, 512, 512, 512, 512, 578, 578, 578, 578, 578, 648, 648, 648, 722, 722, 722, 722, 722, 722, 800, 800, 800, 800, 800, 882, 882, 882

Offset: 1

Lekraj Beedassy, Jun 07 2006

nonn

Charlie Neder, Table of n, a(n) for n = 1..1000

a(14)-a(55) from Charlie Neder, Feb 11 2019

A120089 Square perimeters of primitive Pythagorean triangles.

Original entry on oeis.org

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

Lekraj Beedassy, Jun 07 2006

nonn

Square entries of A024364.

Charlie Neder, Table of n, a(n) for n = 1..1000
P. Yiu, "Primitive Pythagorean triangles with square perimeters" in 'Recreational Mathematics' Chap. 6.2 pp. 50/360

Cf. A120090.

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

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 *)

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

a(n) = A024364(k) = A000290(j) for some k and j. - R. J. Mathar, Jun 08 2006

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

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A120091 Ordered values j of pairs (j,k) that generate A120090.

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A120089 Square perimeters of primitive Pythagorean triangles.

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