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 A343894 Perimeters 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. The triples (a, b, c) are listed in increasing order of side a, and if sides a coincide, in increasing order of side b. 8
 13, 37, 47, 71, 73, 107, 121, 143, 183, 177, 181, 191, 241, 239, 249, 253, 291, 299, 347, 337, 359, 409, 421, 429, 431, 433, 491, 517, 503, 529, 563, 537, 541, 579, 587, 649, 659, 661, 671, 753, 743, 769, 759, 781, 831, 767, 789, 793, 897, 851, 923, 863, 913, 947, 1033, 933 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The triples (a, b, c) are listed in increasing order of side a, and if sides a coincide then in increasing order of side b. The sequence is not monotonic: a(9) = 183 > a(10) = 177. All terms are odd. For the corresponding primitive triples and miscellaneous properties and references, see A343891. LINKS Michel Marcus, Table of n, a(n) for n = 1..1000 FORMULA a(n) = A343891(n, 1) + A343891(n, 2) + A343891(n, 3). a(n) = A020883(n) + A343892(n) + A343893(n). EXAMPLE a(3) = 15 + 12 + 20 = 47, because the third triple is (15, 12, 20) with relations 2/15 = 1/12 + 1/20 and 20-15 < 12 < 20+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 23 23:28 EDT 2021. Contains 345403 sequences. (Running on oeis4.)