S000514


Denominators of a Farey series.

1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 10, 25, 4, 1, 9, 1, 6125, 1029, 1, 1, 33750, 3125, 81, 964467, 2401, 1, 22, 121, 53732704256, 55240493, 117649, 5764801, 169, 2197, 371293, 4826809, 1, 1, 22370117, 14641, 1403076312, 27125634375, 285719, 1666027489

1

S000514

The n-th term of the series is the denominator of the reciprocal of the product of the nonzero terms of F(n) (see Weisstein below). Only a finite number of these terms equal 1. See S000515 for those terms.

T. D. Noe, Plot of 100 terms

T. D. Noe, Table of 100 terms

Jeffrey C. Lagarias and Harsh Mehta, Products of Farey fractions, arXiv 1503.00199 (Mar 01 2015)

Eric W. Weisstein, MathWorld: Farey Sequence

(Mma) FBar[n_] := (prod = 1; Do[If[GCD[h, k] == 1, prod = prod*h/k], {k, n}, {h, k}]; 1/prod); s = Table[FBar[n], {n, 50}]; Denominator[s]

Cf. S000513, S000515.

nonn

T. D. Noe, Mar 03 2015

© Tony D Noe 2014-2015