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 A227042 Triangle of denominators of harmonic mean of n and m, 1 <= m <= n. 7
 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, 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, 17, 9, 19, 10, 21, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See the comments under A227041. a(n,m) gives the denominator of H(n,m) = 2*n*m/(n+m) in lowest terms. LINKS Eric Weisstein's World of Mathematics, Harmonic Mean . FORMULA a(n,m) = denominator(2*n*m/(n+m)), 1 <= m <= n. a(n,m) = (n+m)/gcd(2*n*m, n+m) = (n+m)/gcd(n+m, 2*m^2),  1 <= m <= n. EXAMPLE The triangle of denominators of H(n,m), called a(n,m) begins: n\m  1   2   3   4   5    6    7    8    9   10  11 ... 1:   1 2:   3   1 3:   2   5   1 4:   5   3   7   1 5:   3   7   4   9   1 6:   7   1   1   5  11    1 7:   4   9   5  11   6   13    1 8;   9   5  11   3  13    7   15    1 9:   5  11   2  13   7    5    8   17    1 10: 11   3  13   7   3    2   17    9   19    1 11:  6  13   7  15   8   17    9   19   10   21   1 ... For the triangle of the rationals H(n,m) see the example section of A227041. H(4,2) = denominator(16/6) = denominator(8/3) = 3 = 6/gcd(6,8) = 6/2. CROSSREFS Cf. A277041, A026741 (column m=1), A000265 (m=2), A106619 (m=3), A227140(n+8) (m=4), A227108 (m=5), A221918/A221919. Sequence in context: A134225 A136081 A083106 * A033765 A033777 A329144 Adjacent sequences:  A227039 A227040 A227041 * A227043 A227044 A227045 KEYWORD nonn,easy,frac,tabl AUTHOR Wolfdieter Lang, Jul 01 2013 STATUS approved

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Last modified February 18 04:48 EST 2020. Contains 332011 sequences. (Running on oeis4.)