The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A213544 Sum of numerators of Farey Sequence of order n. 5
 1, 2, 5, 9, 19, 25, 46, 62, 89, 109, 164, 188, 266, 308, 368, 432, 568, 622, 793, 873, 999, 1109, 1362, 1458, 1708, 1864, 2107, 2275, 2681, 2801, 3266, 3522, 3852, 4124, 4544, 4760, 5426, 5768, 6236, 6556, 7376, 7628, 8531, 8971, 9511, 10017, 11098, 11482 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 Wikipedia, Farey Sequence FORMULA a(n) = Sum_{k=1..n} A023896(k). a(n) = A240877(n)/2. - Robert G. Wilson v, Apr 15 2014 a(n) ~ n^3/Pi^2 - Jean-François Alcover, Dec 29 2014 EXAMPLE For n = 3, the Farey Sequence is 0/1, 1/3, 1/2, 2/3, 1/1. Thus a(3) = 0 + 1 + 1 + 2 + 1 = 5. MAPLE with(numtheory): b:= n-> `if`(n=1, 1, n*phi(n)/2): a:= proc(n) option remember; b(n) +`if`(n>1, a(n-1), 0) end: seq(a(n), n=1..60);  # Alois P. Heinz, Jun 14 2012 MATHEMATICA Farey[n_] := Union[ Flatten[ Join[{0}, Table[a/b, {b, n}, {a, b}]]]]; Table[ Total[ Numerator[ Farey[ n]]], {n, 0, 53}] (* Robert G. Wilson v, Apr 15 2014 *) a[n_] := Sum[If[CoprimeQ[j, k], j, 0], {k, 1, n}, {j, 1, k}]; Table[a[n], {n, 1, 48}] (* Jean-François Alcover, Dec 29 2014 *) CROSSREFS Similar to A133404 and A191607. Partial sums of A023896. Cf. A006842, A006843, A240877. Sequence in context: A152546 A286713 A342013 * A265482 A085410 A073118 Adjacent sequences:  A213541 A213542 A213543 * A213545 A213546 A213547 KEYWORD nonn,easy AUTHOR Anunay Kulshrestha, Jun 14 2012 STATUS approved

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

Last modified April 23 01:21 EDT 2021. Contains 343198 sequences. (Running on oeis4.)