%I #11 Feb 18 2014 23:17:51
%S 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,
%T 98,64,27,63,147,81,10,108,288,112,150,180,392,192,162,100,11,175,245,
%U 121,24,44,90,432,800,252,294,320,648,300,242,144,13,99,675,405,363,169,14
%N List the positive rationals in the canonical order A020652(n)/A020653(n) and apply the Sagher map to turn them into integers.
%C 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.
%H Reinhard Zumkeller, <a href="/A060837/b060837.txt">Table of n, a(n) for n = 1..10000</a>
%H Y. Sagher, <a href="http://www.jstor.org/stable/2324846">Counting the rationals</a>, Amer. Math. Monthly, 96 (1989), p. 823. Math. Rev. 90i:04001.
%F 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
%e 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, ...
%o (Haskell)
%o a060837 n = (a020652 n ^ 2) *
%o product (zipWith (^) (a027748_row m)
%o (map ((subtract 1) . (* 2)) (a124010_row m)))
%o where m = a020653 n
%o -- _Reinhard Zumkeller_, Feb 16 2014
%Y Cf. A038566, A071970.
%K nonn,nice,easy
%O 1,2
%A _N. J. A. Sloane_, Jun 19 2002
%E More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jan 12 2003
%E Corrected by _Charles R Greathouse IV_, Sep 02 2009
%E Definition slightly changed by _Reinhard Zumkeller_, Feb 16 2014