A049449 Product of numerator and denominator of fractions in Farey tree A007305/A007306.

0, 1, 2, 3, 6, 4, 10, 15, 12, 5, 14, 24, 21, 28, 40, 35, 20, 6, 18, 33, 30, 44, 65, 60, 36, 45, 84, 104, 77, 70, 88, 63, 30, 7, 22, 42, 39, 60, 90, 85, 52, 70, 133, 168, 126, 119, 152, 112, 55, 66, 144, 209, 170, 198, 273, 228, 126, 117, 204, 234, 165, 130, 154, 99, 42, 8

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• tabf

Comments

Sum of reciprocals of each row (n > 1) equals 1/2. E.g., 1/3 + 1/6, 1/4 + 1/10 + 1/15 + 1/12 and so on. The link to cut-the-knot gives credit to Pierre Lamothe for this observation. - Joshua Zucker, May 11 2006

References

• J. C. Lagarias, Number Theory and Dynamical Systems, pp. 35-72 of S. A. Burr, ed., The Unreasonable Effectiveness of Number Theory, Proc. Sympos. Appl. Math., 46 (1992). Amer. Math. Soc.

Links

• Ivan Neretin, Table of n, a(n) for n = 0..4096
• Alexander Bogomolny, Cut-the-knot on Stern-Brocot trees

Crossrefs

See comment in A119272.

Formula

A007305*A007306.

Extensions

More terms from Megan Wawro (s1095813(AT)cedarville.edu)

More terms from Joshua Zucker, May 11 2006