A227042 - OEIS

A227042

Triangle of denominators of harmonic mean of n and m, 1 <= m <= n.

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

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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. A227041, 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