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A071975 Denominator of rational number i/j such that Sagher map sends i/j to n. 4
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, 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, 18, 55, 28, 57, 58, 59, 15, 61, 62, 7, 1, 65, 66, 67, 17, 69, 70, 71, 4, 73, 74, 3, 19, 77 (list; graph; refs; listen; history; text; internal format)
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.

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]

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Yoram 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+1)/2 if n is odd and f(n)=0 if n is even. - 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[OddQ[a], p^((a+1)/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, v[1, k]^-(-v[2, k]\2), 1))

(Haskell)

a071975 n = product $ zipWith (^) (a027748_row n) $

   map (\e -> (e `mod` 2) * (e + 1) `div` 2) $ a124010_row n

-- Reinhard Zumkeller, Jun 15 2012

CROSSREFS

Cf. A071974.

Cf. A027748, A124010.

Sequence in context: A083346 A065883 A214392 * A182659 A197701 A292770

Adjacent sequences:  A071972 A071973 A071974 * A071976 A071977 A071978

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

STATUS

approved

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Last modified November 21 17:44 EST 2017. Contains 295004 sequences.