A106430 - OEIS

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A106430

Ordered and uniqued length of side opposite the greater of the two angles, one being the double of the other, of a primitive integer-sided triangle.

6, 12, 15, 20, 28, 30, 35, 40, 42, 45, 56, 63, 66, 70, 72, 77, 84, 88, 90, 91, 99, 104, 110, 117, 120, 126, 130, 132, 143, 144, 153, 154, 156, 165, 170, 176, 182, 187, 190, 195, 198, 204, 208, 209, 210, 220, 221, 228, 231, 234, 238, 240, 247, 255, 260, 266, 272, 273, 276, 285, 286, 299

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

This is also the list of a, where a is positive integer solutions of 1/a+1/b=1/c and a>b>c and gcd[a,b,c]=1, sorted by ascending a, then b. See A247372 for list of b, A246429 for list of c. - Albert Lau, Sep 19 2014

LINKS

Albert Lau, Table of n, a(n) for n = 1..10539

FORMULA

Values r*s, where r<s<2r and (r, s)=1.

The other 2 sides are s^2 and r^2-s^2. - Albert Lau, Sep 19 2014

MATHEMATICA

aMax = 300;

Select[Sequence @@@ Table[{m (m + n), n (m + n), m n}, {m, Sqrt[aMax]}, {n, Min[m - 1, aMax/m - m]}], GCD @@ # == 1 &] // Sort;

%[[;; , 1]]

(* Albert Lau, Sep 19 2014 *)

CROSSREFS

Cf. A106499-A106506, A106410, A106420, A247372, A246429