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%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
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