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

1,2

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.

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.

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

Example

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, ...

Prog

(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

Crossrefs

Cf. A038566, A071970.

Sequence in context: A286555 A243353 A182194 * A245452 A019600 A096901

Adjacent sequences: A060834 A060835 A060836 * A060838 A060839 A060840

Keyword

nonn,nice,easy

Author

N. J. A. Sloane, Jun 19 2002

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

Status

approved