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%I #14 Feb 23 2023 11:37:00
%S 1,3,1,2,5,1,5,3,7,1,3,7,4,9,1,7,1,1,5,11,1,4,9,5,11,6,13,1,9,5,11,3,
%T 13,7,15,1,5,11,2,13,7,5,8,17,1,11,3,13,7,3,2,17,9,19,1,6,13,7,15,8,
%U 17,9,19,10,21,1
%N Triangle of denominators of harmonic mean of n and m, 1 <= m <= n.
%C See the comments under A227041. a(n,m) gives the denominator of H(n,m) = 2*n*m/(n+m) in lowest terms.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HarmonicMean.html">Harmonic Mean</a>.
%F a(n,m) = denominator(2*n*m/(n+m)), 1 <= m <= n.
%F a(n,m) = (n+m)/gcd(2*n*m, n+m) = (n+m)/gcd(n+m, 2*m^2), 1 <= m <= n.
%e The triangle of denominators of H(n,m), called a(n,m) begins:
%e n\m 1 2 3 4 5 6 7 8 9 10 11 ...
%e 1: 1
%e 2: 3 1
%e 3: 2 5 1
%e 4: 5 3 7 1
%e 5: 3 7 4 9 1
%e 6: 7 1 1 5 11 1
%e 7: 4 9 5 11 6 13 1
%e 8; 9 5 11 3 13 7 15 1
%e 9: 5 11 2 13 7 5 8 17 1
%e 10: 11 3 13 7 3 2 17 9 19 1
%e 11: 6 13 7 15 8 17 9 19 10 21 1
%e ...
%e For the triangle of the rationals H(n,m) see the example section of A227041.
%e H(4,2) = denominator(16/6) = denominator(8/3) = 3 = 6/gcd(6,8) = 6/2.
%Y Cf. A277041, A026741 (column m=1), A000265 (m=2), A106619 (m=3), A227140(n+8) (m=4), A227108 (m=5), A221918/A221919.
%K nonn,easy,frac,tabl
%O 1,2
%A _Wolfdieter Lang_, Jul 01 2013
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