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A002246
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Given a rational number r = p/q, where q>0, (p,q)=1, define its height to be max{|p|,q}; then a(n) = number of rational numbers of height n.
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4
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3, 4, 8, 8, 16, 8, 24, 16, 24, 16, 40, 16, 48, 24, 32, 32, 64, 24, 72, 32, 48, 40, 88, 32, 80, 48, 72, 48, 112, 32, 120, 64, 80, 64, 96, 48, 144, 72, 96, 64, 160, 48, 168, 80, 96, 88, 184, 64, 168, 80, 128, 96, 208, 72, 160, 96, 144, 112, 232, 64, 240, 120, 144, 128, 192, 80, 264
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The old entry with this sequence number was a duplicate of A008831.
a(n) is also the number of integers prime to n in the interval [n+1, 5n-1]. [From W. Bomfim (webonfim(AT)bol.com.br), Oct 10 2009]
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REFERENCES
| M. N. Huxley, Area, Lattice Points and Exponential Sums, Oxford, 1996; p. 7.
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FORMULA
| a(1) = 3; thereafter a(n) = 4*phi(n) = 4*A000010(n).
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EXAMPLE
| The three rational numbers of height 1 are 0, 1 and -1.
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CROSSREFS
| Cf. A000010, A097080.
Sequence in context: A197138 A065309 A097689 * A030014 A047968 A181778
Adjacent sequences: A002243 A002244 A002245 * A002247 A002248 A002249
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 02 2008
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