|
%I
%S 1,2,3,1,5,6,7,4,1,10,11,3,13,14,15,1,17,2,19,5,21,22,23,12,1,26,9,7,
%T 29,30,31,8,33,34,35,1,37,38,39,20,41,42,43,11,5,46,47,3,1,2,51,13,53,
%U 18,55,28,57,58,59,15,61,62,7,1,65,66,67,17,69,70,71,4,73,74,3,19,77
%N Denominator of rational number i/j such that Sagher map sends i/j to n.
%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.
%C a(n^2) = 1, A071974(n^2) = n, cf. A000290; a(2*(2*n-1)^2) = 2, A071974(2*(2*n-1)^2) = 2*n+1, cf. A077591; A071975(2*(2*n-1)^2) = 2, A071974(2*(2*n-1)^2) = 2*n+1, cf. A077591; [_Reinhard Zumkeller_, Jul 10 2011]
%D Y. Sagher, Counting the rationals, Amer. Math. Monthly, 96 (1989), p. 823. Math. Rev. 90i:04001.
%H _Reinhard Zumkeller_, <a href="/A071975/b071975.txt">Table of n, a(n) for n = 1..10000</a>
%F If n=Product p_i^e_i, then a_n=Product p_i^f(e_i), where f(n)=(n+1)/2 if n is odd and f(n)=0 if n is even - Reiner Martin (reinermartin(AT)hotmail.com), Jul 08 2002
%e The Sagher map sends the following fractions to 1, 2, 3, 4, ...: 1/1, 1/2, 1/3, 2/1, 1/5, 1/6, 1/7, 1/4, 3/1, ...
%t f[{p_, a_}] := If[OddQ[a], p^((a+1)/2), 1]; a[n_] := Times@@(f/@FactorInteger[n])
%o (PARI) a(n)=local(v=factor(n)~); prod(k=1,length(v),if(v[2,k]%2,v[1,k]^-(-v[2,k]\2),1))
%o (Haskell)
%o a071975 n = product $ zipWith (^) (a027748_row n) $
%o map (\e -> (e `mod` 2) * (e + 1) `div` 2) $ a124010_row n
%o -- _Reinhard Zumkeller_, Jun 15 2012
%Y Cf. A071974.
%Y Cf. A027748, A124010.
%K nonn,frac,easy,nice,mult
%O 1,2
%A _N. J. A. Sloane_, Jun 19 2002
%E More terms from Reiner Martin (reinermartin(AT)hotmail.com), Jul 08 2002
|
