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Search: id:A005728
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| A005728 |
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Number of fractions in Farey series of order n (1 + A002088).
(Formerly M0661)
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+0
16
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| 1, 2, 3, 5, 7, 11, 13, 19, 23, 29, 33, 43, 47, 59, 65, 73, 81, 97, 103, 121, 129, 141, 151, 173, 181, 201, 213, 231, 243, 271, 279, 309, 325, 345, 361, 385, 397, 433, 451, 475, 491, 531, 543, 585, 605, 629, 651, 697, 713, 755, 775, 807, 831, 883
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Sometimes called Phi(n).
Leo Moser found an interesting way to generate this sequence, see Gardner.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
M. Gardner, The Last Recreations, 1997, chap 12.
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, a foundation for computer science, Chapter 4.5 - Relative Primality, pages 118 - 120 and Chapter 9 - Asymptotics, Problem 6, pages 448 - 449, Addison-Wesley Publishing Co., Reading, Mass., 1989.
R. K. Guy, The strong law of small numbers. Amer. Math. Monthly 95 (1988), no. 8, 697-712.
W. J. LeVeque, Topics in Number Theory. Addison-Wesley, Reading, MA, 2 vols., 1956, Vol. 1, p. 154.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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a(n) = 1+Sum_{i=1..n} phi(i).
a(n) = n(n+3)/2 - Sum(k = 2 to n, a([n/k])). - David W. Wilson, May 25, 2002
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EXAMPLE
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a(5)=11 because the fractions are 0/1, 1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 1/1.
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MATHEMATICA
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s = 1; Table[s = s + EulerPhi[n], {n, 0, 60}]
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CROSSREFS
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Essentially the same as A049643. Cf. A006843, A002088, A055197, A055201.
Adjacent sequences: A005725 A005726 A005727 this_sequence A005729 A005730 A005731
Sequence in context: A129944 A152900 A079151 this_sequence A049643 A050437 A096246
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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