A337088 Perimeters of integer-sided triangles such that the harmonic mean of their side lengths is an integer.

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

Links

Table of n, a(n) for n=1..71.

Wikipedia, Integer Triangle

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

Adjacent sequences: A337085 A337086 A337087 * A337089 A337090 A337091

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 14 2020

Status

approved