|
| |
|
|
A005728
|
|
Number of fractions in Farey series of order n (1 + A002088).
(Formerly M0661)
|
|
19
| |
|
|
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; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Sometimes called Phi(n).
Leo Moser found an interesting way to generate this sequence, see Gardner.
|
|
|
REFERENCES
| 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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
| 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.
Sameen Ahmed KHAN, Mathematica notebook
|
|
|
FORMULA
| 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
|
|
|
EXAMPLE
| 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.
|
|
|
MATHEMATICA
| Accumulate@ Array[ EulerPhi, 54, 0] + 1
|
|
|
CROSSREFS
| Essentially the same as A049643. Cf. A006843, A002088, A055197, A055201.
Sequence in context: A152900 A079151 * A049643 A050437 A096246 A106639
Adjacent sequences: A005725 A005726 A005727 * A005729 A005730 A005731
|
|
|
KEYWORD
| nonn,easy,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
