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A337091
Perimeters of integer-sided triangles such that the harmonic mean of each pair of its side lengths is an integer.
1
3, 6, 9, 12, 14, 15, 18, 21, 24, 27, 28, 30, 33, 35, 36, 39, 40, 42, 44, 45, 48, 51, 52, 54, 56, 57, 60, 63, 66, 69, 70, 72, 75, 77, 78, 80, 81, 84, 85, 87, 88, 90, 91, 93, 95, 96, 98, 99, 102, 104, 105, 108, 111, 112, 114, 117, 120, 123, 126, 129, 132, 133, 135, 138, 140, 141
OFFSET
1,1
EXAMPLE
6 is in the sequence since each pair of side lengths in the integer triangle [2,2,2] (with perimeter 6) has a harmonic mean of 2 (i.e., 2*2*2/(2+2) = 2).
14 is in the sequence since each pair of side lengths in the integer triangle [2,6,6] (with perimeter 14) has an integer harmonic mean (i.e., 2*2*6/(2+6) = 3, 2*2*6/(2+6) = 3 and 2*6*6/(6+6) = 72/12 = 6).
MATHEMATICA
Table[If[Sum[Sum[(1 - Ceiling[2*k*i/(k + i)] + Floor[2*k*i/(k + i)])*(1- Ceiling[2*k*(n - k - i)/(n - i)] + Floor[2*k*(n - k - i)/(n - i)])*(1 -Ceiling[2*i*(n - k - i)/(n - k)] + Floor[2*i*(n - k - i)/(n - k)])*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}] > 0, n, {}], {n, 150}] // Flatten
CROSSREFS
Cf. A337088.
Sequence in context: A230215 A120688 A102014 * A168045 A288522 A226894
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Aug 15 2020
STATUS
approved