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%I #13 Jun 01 2017 19:31:20
%S 0,3,12,3,24,15,4,21,48,9,60,33,24,39,84,5,96,51,36,57,120,21,132,69,
%T 16,75,156,27,168,87,60,93,192,11,204,105,72,111,228,39,240,123,28,
%U 129,264,45,276,141,96,147,300,17,312,159,108,165,336,57,348,177
%N Numerators of harmonic mean H(n,3), n >= 0.
%C a(n) = numerator(H(n,3)) = numerator(6*n/(n+3)), n>=0, with H(n,3) the harmonic mean of n and 3.
%C The corresponding denominators are given in A106619(n+3), n >= 0.
%C a(n+3), n>=0, is the third column (m=3) of the triangle A227041.
%F a(n) = numerator(6*n/(n+3)), n >= 0.
%F a(n) = 6*n/gcd(n+3,6*n) = 6*n/gcd(n+3,18), n >= 0.
%e The rationals H(n,3) begin: 0, 3/2, 12/5, 3, 24/7, 15/4, 4, 21/5, 48/11, 9/2, 60/13, 33/7, 24/5, 39/8, 84/17, 5, ...
%t Table[Numerator[HarmonicMean[{n,3}]],{n,0,60}] (* _Harvey P. Dale_, Jun 01 2017 *)
%Y A227041(n+3,3), A106619(n+3) (denominator), n >= 0.
%K nonn,frac,easy
%O 0,2
%A _Wolfdieter Lang_, Jul 01 2013