Search: id:A005728
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%I A005728 M0661
%S A005728 1,2,3,5,7,11,13,19,23,29,33,43,47,59,65,73,81,97,103,121,129,141,
%T A005728 151,173,181,201,213,231,243,271,279,309,325,345,361,385,397,433,
%U A005728 451,475,491,531,543,585,605,629,651,697,713,755,775,807,831,883
%N A005728 Number of fractions in Farey series of order n (1 + A002088).
%C A005728 Sometimes called Phi(n).
%C A005728 Leo Moser found an interesting way to generate this sequence, see Gardner.
%D A005728 M. Gardner, The Last Recreations, 1997, chap 12.
%D A005728 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.
%D A005728 R. K. Guy, The strong law of small numbers. Amer. Math. Monthly 95 (1988), 
               no. 8, 697-712.
%D A005728 W. J. LeVeque, Topics in Number Theory. Addison-Wesley, Reading, MA, 
               2 vols., 1956, Vol. 1, p. 154.
%D A005728 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005728 T. D. Noe, <a href="b005728.txt">Table of n, a(n) for n=0..1000</a>
%H A005728 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               FareySequence.html">Link to a section of The World of Mathematics.</
               a>
%F A005728 a(n) = 1+Sum_{i=1..n} phi(i).
%F A005728 a(n) = n(n+3)/2 - Sum(k = 2 to n, a([n/k])). - David W. Wilson, May 25, 
               2002
%e A005728 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.
%t A005728 s = 1; Table[s = s + EulerPhi[n], {n, 0, 60}]
%Y A005728 Essentially the same as A049643. Cf. A006843, A002088, A055197, A055201.
%Y A005728 Sequence in context: A129944 A152900 A079151 this_sequence A049643 A050437 
               A096246
%Y A005728 Adjacent sequences: A005725 A005726 A005727 this_sequence A005729 A005730 
               A005731
%K A005728 nonn,easy,nice
%O A005728 0,2
%A A005728 N. J. A. Sloane (njas(AT)research.att.com).

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