A337244 Perimeters of integer-sided triangles such that the harmonic mean of all the side lengths and the harmonic mean of each pair of side lengths is an integer.

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 70, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 140, 141, 144, 147, 150, 153, 156, 159, 162, 165, 168, 171, 174, 177, 180, 183, 186

Offset

1,1

Links

Table of n, a(n) for n=1..64.

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), and the harmonic mean of each pair of side lengths has harmonic mean 2*2*2/(2+2) = 2 (an integer).
14 is not in the sequence. Although 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), the harmonic mean of all the side lengths is 3*2*6*6/(2*6+2*6+6*6) = 216/60 = 18/5 (not an integer).

Crossrefs

Cf. A337088, A337091.

Sequence in context: A161351 A328168 A209258 * A366847 A031193 A296515

Adjacent sequences: A337241 A337242 A337243 * A337245 A337246 A337247

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 20 2020

Status

approved