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 A343892 Side b of integer-sided primitive triangles (a, b, c) 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. 7
 3, 10, 12, 15, 21, 30, 36, 35, 40, 44, 55, 56, 52, 63, 65, 78, 70, 90, 77, 105, 99, 85, 102, 119, 132, 136, 117, 114, 143, 133, 126, 152, 171, 154, 182, 168, 165, 210, 195, 161, 176, 184, 208, 207, 187, 240, 230, 253, 200, 221, 198, 255, 225, 234, 216, 275, 300, 306, 247, 270 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The triples (a, b, c) are displayed in increasing order of side a, and if sides a coincide then in increasing order of the side b. The sequence is not increasing because a(7) = 36 > a(8) = 35, but, these sides b are proposed in increasing order in A020890. The first term appearing twice is 330 and corresponds to triples (435, 330, 638) and (460, 330, 759), the second one is 462 and corresponds to triples (483, 462, 506) and (532, 462, 627). For the corresponding primitive triples and miscellaneous properties and references, see A343891. LINKS FORMULA a(n) = A343891(n, 2). EXAMPLE a(4) = 15, because the fourth triple is (21, 15, 35) with side b = 15, satisfying 1/15 = 2/21 - 1/35 and 31-15 < 21 < 31+15. MAPLE for a from 4 to 200 do for b from floor(a/2)+1 to a-1 do c := a*b/(2*b-a); if c=floor(c) and igcd(a, b, c)=1 and c-b

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Last modified June 21 00:35 EDT 2021. Contains 345328 sequences. (Running on oeis4.)