A092824 - OEIS

%I #7 Nov 21 2013 13:11:40

%S 1,2,3,4,6,8,12,16,18,24,30,40,48,60,72,80,90,96,120,144,180,240,288,

%T 360,432,480,540,576,600,720,840,1008,1260,1440,1680,2016,2160,2520,

%U 2880,3024,3360,3600,3780,4032,4200,4320,5040,5760,6720,8064,10080

%N Farey-factorial numerators.

%C 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.

%F 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.

%e The sequence begins with these segments:

%e 1

%e 2

%e 3 4 6

%e 8 12 16 18 24

%e For the next segment, start with these Farey

%e fractions of order 5:

%e 1/4 1/3 2/5 1/2 3/5 2/3 3/4 4/5 5/5.

%e Multiply these by 5! to get

%e 30 40 48 60 72 80 90 96 120.

%t 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 *)

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

%K nonn

%O 1,2

%A _Clark Kimberling_, Mar 06 2004