login
This site is supported by donations to The OEIS Foundation.

 

Logo

Invitation: celebrating 50 years of OEIS, 250000 sequences, and Sloane's 75th, there will be a conference at DIMACS, Rutgers, Oct 9-10 2014.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A005728 Number of fractions in Farey series of order n; a(n) = 1 + A002088(n).
(Formerly M0661)
35
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, 901, 941, 965 (list; graph; refs; listen; history; text; 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.

S. A. Khan, How Many Equivalent Resistances?, RESONANCE, May 2012; http://www.ias.ac.in/resonance/May2012/p468-475.pdf. - From N. J. A. Sloane, Oct 15 2012

S. A. Khan, Farey sequences and resistor networks, Proc. Indian Acad. Sci. (Math. Sci.) Vol. 122, No. 2, May 2012, pp. 153-162. - From N. J. A. Sloane, Oct 23 2012

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

Sameen Ahmed KHAN, Mathematica notebook

Eric Weisstein's World of Mathematics, Farey Sequence.

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

a(n) = a(n-1) + phi(n) with a(0) = 1. - Arkadiusz Wesolowski, Oct 13 2012

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

PROG

(Haskell)

a005728 n = a005728_list

a005728_list = scanl (+) 1 a000010_list

-- Reinhard Zumkeller, Aug 04 2012

(PARI) a(n)=1+sum(k=1, n, eulerphi(k)) \\ Charles R Greathouse IV, Jun 03 2013

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.

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified September 18 09:40 EDT 2014. Contains 246899 sequences.