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).
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
Offset: 1
Keywords
Links
- 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 ...).
Programs
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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 *) -
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));