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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(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.
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
KEYWORD
nonn
AUTHOR
STATUS
approved

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