%I #41 Feb 03 2023 11:35:17

%S 6,15,20,28,35,42,45,63,66,72,77,88,91,99,104,110,117,120,130,143,153,

%T 156,165,170,187,190,195,204,209,210,221,228,231,238,247,255,266,272,

%U 273,276,285,299,304,322,323,325,336,342,345,350,357,368,378,391,399

%N Ordered semiperimeters of primitive Pythagorean triangles.

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

%C 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

%H Ray Chandler, <a href="/A020886/b020886.txt">Table of n, a(n) for n = 1..10000</a> (duplicates removed by Sean A. Irvine)

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

%p 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

%t A078926[n_] := Sum[Boole[n < d^2 < 2n && CoprimeQ[d, n/d]], {d, Divisors[ n/2^IntegerExponent[n, 2]]}];

%t Select[Range[1000], A078926[#]>0&] (* _Jean-François Alcover_, Mar 23 2020 *)

%o (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

%o 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

%Y Subsequence of A005279.

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

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

%K nonn

%O 1,1

%A _Clark Kimberling_