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 A071974 Numerator of rational number i/j such that Sagher map sends i/j to n. 4
 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 4, 1, 3, 1, 2, 1, 1, 1, 1, 5, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 4, 7, 5, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 8, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 5, 2, 1, 1, 1, 4, 9, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 7, 3, 10, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 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. a(n^2) = n, A071975(n^2) = 1, cf. A000290; a(2*(2*n-1)^2) = 2*n+1, A071975(2*(2*n-1)^2) = 2, cf. A077591; [Reinhard Zumkeller, Jul 10 2011] LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 David M. Bradley, Counting the Positive Rationals: A Brief Survey, arXiv:math/0509025 Gerald Freilich, A denumerability formula for the rationals, Amer. Math. Monthly, Nov 1965, p1013-1014 Kevin McCrimmon, Enumeration of the positive rationals, Amer. Math. Monthly, Nov 1960, p868. Y. Sagher, Counting the rationals, Amer. Math. Monthly, 96 (1989), p. 823. Math. Rev. 90i:04001. FORMULA If n=Product p_i^e_i, then a_n=Product p_i^f(e_i), where f(n)=n/2 if n is even and f(n)=0 if n is odd - Reiner Martin (reinermartin(AT)hotmail.com), Jul 08 2002 EXAMPLE 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, ... MATHEMATICA f[{p_, a_}] := If[EvenQ[a], p^(a/2), 1]; a[n_] := Times@@(f/@FactorInteger[n]) PROG (PARI) a(n)=local(v=factor(n)~); prod(k=1, length(v), if(v[2, k]%2, 1, v[1, k]^(v[2, k]/2))) (Haskell) a071974 n = product \$ zipWith (^) (a027748_row n) \$    map (\e -> (1 - e `mod` 2) * e `div` 2) \$ a124010_row n -- Reinhard Zumkeller, Jun 15 2012 CROSSREFS Cf. A071975. Differs from A056622 at a(32). Cf. A027748, A124010. Sequence in context: A162154 A134505 A076933 * A056622 A237983 A254613 Adjacent sequences:  A071971 A071972 A071973 * A071975 A071976 A071977 KEYWORD nonn,frac,easy,nice,mult AUTHOR N. J. A. Sloane, Jun 19 2002 EXTENSIONS More terms from Reiner Martin (reinermartin(AT)hotmail.com), Jul 08 2002 Additional references supplied by Kevin Ryde added by N. J. A. Sloane, May 31 2012 STATUS approved

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Last modified October 15 05:56 EDT 2018. Contains 316202 sequences. (Running on oeis4.)