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