OFFSET

1,1

LINKS

Wikipedia, Integer Triangle

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

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Aug 15 2020

STATUS

approved