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A020886
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Ordered semiperimeters of primitive Pythagorean triangles.
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31
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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MAPLE
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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
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MATHEMATICA
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A078926[n_] := Sum[Boole[n < d^2 < 2n && CoprimeQ[d, n/d]], {d, Divisors[ n/2^IntegerExponent[n, 2]]}];
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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