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A015614
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Sum( phi(i), i=1..n) - 1.
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9
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0, 1, 3, 5, 9, 11, 17, 21, 27, 31, 41, 45, 57, 63, 71, 79, 95, 101, 119, 127, 139, 149, 171, 179, 199, 211, 229, 241, 269, 277, 307, 323, 343, 359, 383, 395, 431, 449, 473, 489, 529, 541, 583, 603, 627, 649, 695, 711, 753, 773, 805, 829, 881, 899, 939, 963
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Number of elements in the set {(x,y): 1<=x<y<=n, 1=gcd(x,y)}; number of fractions in (Haros)-Farey series of order n.
The asymptotic limit for the sequence is a(n) ~ 3*n^2/Pi^2. - Martin Renner, Dec 12 2011
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REFERENCES
| Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966, p. 170-171.
James J. Sylvester, On the number of fractions contained in any Farey series of which the limiting number is given, in: London, Edinburgh and Dublin Philosophical Magazine (5th series) 15 (1883), p. 251.
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FORMULA
| a(n) = A002088(n) - 1.
a(n) = (A018805(n) - 1)/2. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 08 2006
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CROSSREFS
| Cf. A002088, A018805, column 2 of triangle A186974.
Sequence in context: A056533 A114186 A117992 * A138203 A007952 A145819
Adjacent sequences: A015611 A015612 A015613 * A015615 A015616 A015617
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KEYWORD
| nonn
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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EXTENSIONS
| More terms from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 08 2006
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