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A049643
Number of fractions in Farey series of order n.
6
0, 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
OFFSET
0,2
COMMENTS
Essentially the same as A005728.
LINKS
R. K. Guy, The strong law of small numbers. Amer. Math. Monthly 95 (1988), no. 8, 697-712.
N. J. A. Sloane, Families of Essentially Identical Sequences, Mar 24 2021 (Includes this sequence)
FORMULA
a(n) = A049641(2*n).
From G. C. Greubel, Dec 13 2017: (Start)
a(n) = 1 + Sum_{k=1..n} phi(k), with a(0)=0.
a(n) = A005728(n) for n >= 1. (End)
a(n) = a(n-1) + phi(n) for n > 1. - Robert G. Wilson v, Dec 13 2017
MATHEMATICA
a[0] = 0; a[n_] := 1 + Sum[EulerPhi[k], {k, 1, n}]; Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Nov 27 2015 *)
a[0] = 0; a[1] = 2; a[n_] := a[n -1] + EulerPhi[n]; Array[a, 55, 0] (* Robert G. Wilson v, Dec 13 2017 *)
Join[{0}, Rest[Accumulate[EulerPhi[Range[0, 60]]]+1]] (* Harvey P. Dale, Oct 16 2018 *)
a[n_] := If[n == 0, 0, FareySequence[n] // Length];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Jul 16 2022 *)
PROG
(PARI) for(n=0, 30, print1(if(n==0, 0, 1+sum(k=1, n, eulerphi(k))), ", ")) \\ G. C. Greubel, Dec 06 2017
(Magma) [0] cat [n le 1 select 2 else Self(n-1)+EulerPhi(n): n in [1..60]]; // G. C. Greubel, Dec 06 2017
CROSSREFS
Cf. A000010.
Sequence in context: A152900 A079151 A274335 * A005728 A050437 A096246
KEYWORD
nonn,easy,nice
STATUS
approved