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A071975
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Denominator of rational number i/j such that Sagher map sends i/j to n.
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4
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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; internal format)
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OFFSET
| 1,2
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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]
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REFERENCES
| Y. Sagher, Counting the rationals, Amer. Math. Monthly, 96 (1989), p. 823. Math. Rev. 90i:04001.
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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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
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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, ...
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MATHEMATICA
| f[{p_, a_}] := If[OddQ[a], p^((a+1)/2), 1]; a[n_] := Times@@(f/@FactorInteger[n])
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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))
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CROSSREFS
| Cf. A071974.
Sequence in context: A007913 A083346 A065883 * A182659 A197701 A055905
Adjacent sequences: A071972 A071973 A071974 * A071976 A071977 A071978
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KEYWORD
| nonn,frac,easy,nice,mult
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jun 19 2002
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EXTENSIONS
| More terms from Reiner Martin (reinermartin(AT)hotmail.com), Jul 08 2002
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