A071970 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.

1, 2, 4, 3, 18, 12, 9, 8, 48, 45, 50, 20, 75, 72, 16, 5, 200, 112, 147, 288, 320, 175, 98, 28, 245, 800, 192, 63, 392, 80, 25, 6, 180, 675, 648, 176, 847, 490, 300, 99, 3872, 832, 845, 600, 1008, 1323, 162, 108, 567, 1176, 720, 325, 5408, 704, 363, 90, 700, 539

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 is multiplicative.

Examples

			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, ...
		

Links

• Y. Sagher, Counting the rationals, Amer. Math. Monthly, 96 (1989), p. 823.

Crossrefs

Cf. A002487, A060837.

Programs

Mathematica

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 *)

PARI

s(n)=if(n<2,n>0,if(n%2,s((n+1)/2)+s((n-1)/2),s(n/2))) /* A002487(n) */

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)

Extensions

More terms from Michael Somos, Jul 19 2002