The index of the terms in a Farey sequence that are integers.
1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 16, 18, 21, 22, 28, 39, 40, 57, 58
1
Derksen and Lagarias prove that 58 is the last term of this finite sequence.
T. D. Noe, Plot of 19 terms
H. Derksen and J. C. Lagarias, Problem 11601 (The product of Farey series), Amer. Math. Monthly 118 (2011), no. 9, 846. [Solution 120 (2013), 857-858.]
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, 100}]; Flatten[Position[s, _?(IntegerQ[#] &)]]
Cf. S000513, S000514, S000516.
nonn,fini,full
T. D. Noe, Mar 03 2015