A020886 Ordered semiperimeters of primitive Pythagorean triangles.

6, 15, 20, 28, 35, 42, 45, 63, 66, 72, 77, 88, 91, 99, 104, 110, 117, 120, 130, 143, 153, 156, 165, 170, 187, 190, 195, 204, 209, 210, 221, 228, 231, 238, 247, 255, 266, 272, 273, 276, 285, 299, 304, 322, 323, 325, 336, 342, 345, 350, 357, 368, 378, 391, 399

Offset

1,1

Comments

k is in this sequence iff A078926(k) > 0.

Also, ordered sides c of primitive triples (a, b, c) for integer-sided triangles where side a is the harmonic mean of the 2 other sides b and c, i.e., 2/a = 1/b + 1/c with b < a < c (A343893). - Bernard Schott, May 06 2021

Links

Ray Chandler, Table of n, a(n) for n = 1..10000 (duplicates removed by Sean A. Irvine)

Formula

a(n) = A024364(n)/2.

Maple

isA020886 := proc(an) local r::integer, s::integer ; for r from floor((an/2)^(1/2)) to floor(an^(1/2)) do for s from r-1 to 1 by -2 do if r*(r+s) = an and gcd(r, s) < 2 then RETURN(true) ; fi ; if r*(r+s) < an then break ; fi ; od ; od : RETURN(false) ; end : for n from 2 to 400 do if isA020886(n) then printf("%d, ", n) ; 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]]}];
Select[Range[1000], A078926[#]>0&] (* Jean-François Alcover, Mar 23 2020 *)

Prog

(PARI) is(n, f=factor(n))=my(P=apply(i->f[i, 1]^f[i, 2], [2-n%2..#f~]), nn=2*n); forvec(v=vector(#P, i, [0, 1]), my(d=prod(i=1, #v, P[i]^v[i]), d2=d^2); if(d2<nn && d2>n, return(1))); 0
list(lim)=my(v=List()); forfactored(n=6, lim\1, if(is(n[1], n[2]), listput(v, n[1]))); Vec(v) \\ Charles R Greathouse IV, Feb 03 2023

Crossrefs

Subsequence of A005279.

Cf. A024364, A078926, A020882, A020884, A020885.

Triangles with 2/a = 1/b + 1/c: A343891 (triples), A020883 (side a), A343892 (side b), A343893 (side c), A343894 (perimeter).

Sequence in context: A044439 A348866 A128253 * A093508 A302022 A094183

Adjacent sequences: A020883 A020884 A020885 * A020887 A020888 A020889

Keyword

nonn

Author

Clark Kimberling

Status

approved