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A092824 Farey-factorial numerators. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A326712 A191612 A048874 * A084094 A217689 A018718

Adjacent sequences:  A092821 A092822 A092823 * A092825 A092826 A092827

KEYWORD

nonn

AUTHOR

Clark Kimberling, Mar 06 2004

STATUS

approved

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Last modified December 9 05:44 EST 2021. Contains 349627 sequences. (Running on oeis4.)