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A337088
Perimeters of integer-sided triangles such that the harmonic mean of their side lengths is an integer.
2
3, 6, 9, 10, 12, 13, 15, 18, 20, 21, 24, 26, 27, 28, 30, 31, 33, 35, 36, 37, 39, 40, 42, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 65, 66, 69, 70, 71, 72, 73, 74, 75, 77, 78, 80, 81, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 96, 97, 98, 99, 100, 101, 102, 104
OFFSET
1,1
EXAMPLE
6 is in the sequence since the integer-sided triangle [2,2,2] (with perimeter 6) has harmonic mean 3*2*2*2/(2*2+2*2+2*2) = 2 (an integer).
10 is in the sequence since the triangle [2,4,4] (with perimeter 10) has harmonic mean 3*2*4*4/(2*4+2*4+4*4) = 96/32 = 3 (an integer).
MATHEMATICA
Table[If[Sum[Sum[(1 - Ceiling[3*i*k*(n - i - k)/(i*k + k*(n - i - k) + i*(n - i - k))] + Floor[3*i*k*(n - i - k)/(i*k + k*(n - i - k) + i*(n - i - k))]) Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}] > 0, n, {}], {n, 100}] // Flatten
CROSSREFS
Cf. A337086.
Sequence in context: A309584 A081605 A293828 * A110263 A022304 A176423
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Aug 14 2020
STATUS
approved