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A213544 Sum of numerators of Farey Sequence of order n. 4
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: A293329 A152546 A286713 * A265482 A085410 A073118

Adjacent sequences:  A213541 A213542 A213543 * A213545 A213546 A213547

KEYWORD

nonn,easy

AUTHOR

Anunay Kulshrestha, Jun 14 2012

STATUS

approved

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Last modified April 23 03:26 EDT 2019. Contains 322380 sequences. (Running on oeis4.)