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 A020886 Ordered semiperimeters of primitive Pythagorean triangles. 31
 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 (list; graph; refs; listen; history; text; internal format)
 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(d2n, 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

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Last modified April 14 18:28 EDT 2024. Contains 371667 sequences. (Running on oeis4.)