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

1,2

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 is multiplicative.

Links

Table of n, a(n) for n=1..58.

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

Example

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, ...

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 *)

Prog

(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)

Crossrefs

Cf. A002487, A060837.

Sequence in context: A132049 A229213 A356063 * A182103 A303053 A163089

Adjacent sequences: A071967 A071968 A071969 * A071971 A071972 A071973

Keyword

nonn,nice,easy

Author

N. J. A. Sloane, Jun 19 2002

Extensions

More terms from Michael Somos, Jul 19 2002

Status

approved