A060837 List the positive rationals in the canonical order A020652(n)/A020653(n) and apply the Sagher map to turn them into integers.

1, 2, 4, 3, 9, 8, 12, 18, 16, 5, 25, 6, 20, 72, 48, 50, 36, 7, 45, 75, 49, 32, 28, 80, 200, 98, 64, 27, 63, 147, 81, 10, 108, 288, 112, 150, 180, 392, 192, 162, 100, 11, 175, 245, 121, 24, 44, 90, 432, 800, 252, 294, 320, 648, 300, 242, 144, 13, 99, 675, 405, 363, 169, 14

Offset: 1

Author

N. J. A. Sloane, Jun 19 2002

Keywords

• nonn
• nice
• easy

Comments

The Sagher map sends Product p_i^e_i / Product q_i^f_i (p_i and q_i being distinct primes) to Product p_i^(2e_i) * Product q_i^(2f_i-1). This map is multiplicative.

Examples

			The first few rationals and their images are 1/1 -> 1, 1/2 -> 2, 2/1 -> 4, 1/3 -> 3, 3/1 -> 9, 1/4 -> 8, ...
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Y. Sagher, Counting the rationals, Amer. Math. Monthly, 96 (1989), p. 823. Math. Rev. 90i:04001.

Crossrefs

Cf. A038566, A071970.

Programs

Haskell

a060837 n = (a020652 n ^ 2) *
   product (zipWith (^) (a027748_row m)
                        (map ((subtract 1) . (* 2)) (a124010_row m)))
   where m = a020653 n
-- Reinhard Zumkeller, Feb 16 2014

Formula

a(n) = A020652(n)^2 * product(A027748(m,k)^(2*A124010(m,k)-1): m=a020653(n), k=1..A000005(m)). - Reinhard Zumkeller, Feb 16 2014

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jan 12 2003

Corrected by Charles R Greathouse IV, Sep 02 2009

Definition slightly changed by Reinhard Zumkeller, Feb 16 2014