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A244396 a(n) = Sum_{k=1, n} phi(k)*index(k, n), with phi(k) the Euler totient A000010(k) and index(k,n) the position of 1/k in the n-th row of the Farey sequence of order k, A049805(n,k). 0
2, 5, 12, 21, 39, 54, 87, 117, 162, 204, 279, 333, 435, 516, 624, 732, 900, 1017, 1224, 1380, 1590, 1785, 2082, 2286, 2616, 2886, 3237, 3543, 4005, 4305, 4830, 5238, 5748, 6204, 6816, 7266, 8004, 8571, 9279, 9879, 10779, 11373, 12360, 13110, 14010, 14835 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..46.

R. Tomás, From Farey sequences to resonance diagrams, Phys. Rev. ST Accel. Beams 17, 014001 - Published 29 January 2014.

R. Tomás, Asymptotic behavior of a series of Euler's Totient function times the cardinality of truncated Farey sequences, arXiv:1406.6991 [math.NT], 2014 (see Chapter 5, Evaluating ...).

FORMULA

a(n) = Sum_{k=1, n} A000010(k)*A049805(k, n).

a(n) = n^3/(6*zeta(3)) + O(n^2). (see (22) in Tomás link).

MATHEMATICA

a[n_] := With[{f = FareySequence[n]}, Sum[EulerPhi[k] FirstPosition[f, 1/k ][[1]], {k, 1, n}]]; Array[a, 50] (* Jean-François Alcover, Sep 26 2018 *)

PROG

(PARI) farey(n) = {vf = [0]; for (k=1, n, for (m=1, k, vf = concat(vf, m/k); ); ); vecsort(Set(vf)); }

a(n) = my(row = farey(n)); sum(k=1, n, eulerphi(k)*vecsearch(row, 1/k));

CROSSREFS

Cf. A000010, A049805, A006842, A006843.

Sequence in context: A307605 A079648 A080838 * A182993 A238741 A218904

Adjacent sequences:  A244393 A244394 A244395 * A244397 A244398 A244399

KEYWORD

nonn

AUTHOR

Michel Marcus, Jun 27 2014

STATUS

approved

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Last modified October 28 02:07 EDT 2021. Contains 348307 sequences. (Running on oeis4.)