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%I #12 Oct 03 2017 03:32:50
%S 1,2,4,3,18,12,9,8,48,45,50,20,75,72,16,5,200,112,147,288,320,175,98,
%T 28,245,800,192,63,392,80,25,6,180,675,648,176,847,490,300,99,3872,
%U 832,845,600,1008,1323,162,108,567,1176,720,325,5408,704,363,90,700,539
%N List the positive rationals in the order in which they are produced by the Stern sequence A002487 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 is multiplicative.
%H Y. Sagher, <a href="http://www.jstor.org/stable/2324846">Counting the rationals</a>, Amer. Math. Monthly, 96 (1989), p. 823.
%e The first few rationals and their images are 1/1 -> 1, 1/2 -> 2, 2/1 -> 4, 1/3 -> 3, 3/2 -> 18, 2/3 -> 12, 3/1 -> 9, 1/4 -> 8, ...
%t nmax = 58; s[0] = 0; s[1] = 1; s[n_?EvenQ] := s[n/2]; s[n_] := s[(n-1)/2] + s[(n+1)/2]; v = Table[ FactorInteger /@ {s[n] , s[n+1]}, {n, 1, nmax}]; a[n_] := Times @@ (#[[1]]^(2*#[[2]])&) /@ v[[n, 1]]*Times @@ (#[[1]]^(2*#[[2]]-1)&) /@ v[[n, 2]]; Table[a[n], {n, 1, nmax}] (* _Jean-François Alcover_, Nov 25 2011, after Pari *)
%o (PARI) s(n)=if(n<2,n>0,if(n%2,s((n+1)/2)+s((n-1)/2),s(n/2))) /* A002487(n) */
%o (PARI) a(n)=local(v); if(n,v=factor(s(n)/s(n+1))~; prod(k=1,length(v),v[1,k]^if(v[2,k]<0,-1-2*v[2,k],2*v[2,k])),0)
%Y Cf. A002487, A060837.
%K nonn,nice,easy
%O 1,2
%A _N. J. A. Sloane_, Jun 19 2002
%E More terms from _Michael Somos_, Jul 19 2002
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