This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A092824 #11 May 13 2025 02:41:18
%S A092824 1,2,3,4,6,8,12,16,18,24,30,40,48,60,72,80,90,96,120,144,180,240,288,
%T A092824 360,432,480,540,576,600,720,840,1008,1260,1440,1680,2016,2160,2520,
%U A092824 2880,3024,3360,3600,3780,4032,4200,4320,5040,5760,6720,8064,10080
%N A092824 Farey-factorial numerators.
%C A092824 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 A092824 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 A092824 The sequence begins with these segments:
%e A092824 1
%e A092824 2
%e A092824 3 4 6
%e A092824 8 12 16 18 24
%e A092824 For the next segment, start with these Farey fractions of order 5:
%e A092824 1/4 1/3 2/5 1/2 3/5 2/3 3/4 4/5 5/5.
%e A092824 Multiply these by 5! to get
%e A092824 30 40 48 60 72 80 90 96 120.
%t A092824 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 A092824 Cf. A000142, A001048, A015614, A059171, A052747.
%K A092824 nonn
%O A092824 1,2
%A A092824 _Clark Kimberling_, Mar 06 2004