A092824 Farey-factorial numerators.

1, 2, 3, 4, 6, 8, 12, 16, 18, 24, 30, 40, 48, 60, 72, 80, 90, 96, 120, 144, 180, 240, 288, 360, 432, 480, 540, 576, 600, 720, 840, 1008, 1260, 1440, 1680, 2016, 2160, 2520, 2880, 3024, 3360, 3600, 3780, 4032, 4200, 4320, 5040, 5760, 6720, 8064, 10080

Offset

1,2

Comments

The last number in the n-th segment is n!. Let f(n) be the first number in segment n; except for initial terms, f is A001048 and A059171. Let g(n) be the second number in segment n; except for initial terms, g is A052747. Except for the initial terms, the number of numbers in segment n is given by A015614.

Links

Table of n, a(n) for n=1..51.

Formula

Let S(n) be the set of integers an!/b, where a/b ranges through the positive Farey fractions of order n. A092824 is the increasing sequence of integers in the union of the sets S(n), for n>=1.

Example

The sequence begins with these segments:
1
2
3 4 6
8 12 16 18 24
For the next segment, start with these Farey
fractions of order 5:
1/4 1/3 2/5 1/2 3/5 2/3 3/4 4/5 5/5.
Multiply these by 5! to get
30 40 48 60 72 80 90 96 120.

Mathematica

f[n_] := n! * Table[a/b, {b, 1, n}, {a, 1, b}] // Flatten // Union // Rest; Flatten[Table[f[n], {n, 1, 8}] /. {} -> {1}][[1 ;; 51]] (* Jean-François Alcover, May 18 2011 *)

Crossrefs

Cf. A000142, A001048, A015614, A059171, A052747.

Sequence in context: A191612 A362668 A048874 * A355578 A084094 A217689

Adjacent sequences: A092821 A092822 A092823 * A092825 A092826 A092827

Keyword

nonn

Author

Clark Kimberling, Mar 06 2004

Status

approved