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Farey-factorial numerators, including duplicates.
2

%I #4 Jul 12 2012 00:39:48

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

%T 180,240,288,360,432,480,540,576,600,720,720,840,1008,1260,1440,1680,

%U 2016,2160,2520,2880,3024,3360,3600,3780,4032,4200,4320,5040,5040,5760

%N Farey-factorial numerators, including duplicates.

%C The only repeated terms are 1!, 2!, 3!, etc. Deleting one of each leaves A092824. When written as an array with (row n)=n!*(Farey fractions of order n), The row sums are given by A093593. The n-th alternating row sum is n!/2, for n>=2. (2/n!)*(n-th row sum)=A005728(n)=number of Farey fractions of order n.

%e Put the positive Farey fractions of order n into row n,

%e and multiply by n!:

%e 1

%e 1 2

%e 2 3 4 6

%e 6 8 12 16 18 24 ...

%e Link the rows to form the sequence.

%Y Cf. A005728, A092824, A093593.

%K nonn,tabf

%O 1,3

%A _Clark Kimberling_, Apr 03 2004