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A071974
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Numerator of rational number i/j such that Sagher map sends i/j to n.
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4
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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; internal format)
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OFFSET
| 1,4
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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) = 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]
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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/2 if n is even and f(n)=0 if n is odd - 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[EvenQ[a], p^(a/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, 1, v[1, k]^(v[2, k]/2)))
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CROSSREFS
| Cf. A071975. Differs from A056622 at a(32).
Sequence in context: A162154 A134505 A076933 * A056622 A129265 A030358
Adjacent sequences: A071971 A071972 A071973 * A071975 A071976 A071977
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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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