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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

Table of n, a(n) for n=1..66.

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.)