A092824 -id:A092824 - cp's OEIS frontend

A093593 n! times sum of Farey fractions of order n.

1, 3, 15, 84, 660, 4680, 47880, 463680, 5261760, 59875200, 858211200, 11256537600, 183697113600, 2833294464000, 47730114432000, 847372990464000, 17250840262656000, 329722245844992000, 7359528574734336000, 156922179527393280000, 3601911423105515520000, 84862054947209379840000

Offset: 1

Clark Kimberling, Apr 03 2004

nonn

			Multiplication of n-th-order positive Farey fractions by n! gives the integer sequence A002088(n), for n>=1. Arrange them in rows:
1
1 2
2 3 4 6
6 8 12 16 18 24
The sum over row 4 is a(4)=84.

Eric Weisstein's World of Mathematics, Farey Sequence.

Cf. A002088, A092824, A093594.

Farey[n_] := Union[ Flatten[ Join[{0}, Table[a/b, {b, n}, {a, b}]]]]; Table[n!Plus @@ Farey[n], {n, 0, 20}] (* Robert G. Wilson v, Apr 06 2004 *)

a(n) = my(list = List()); for (k=1, n, for (m=1, k, listput(list, m/k); ); ); n!*vecsum(Set(Vec(list))); \\ Michel Marcus, Mar 01 2023

More terms from Robert G. Wilson v, Apr 06 2004

More terms from Michel Marcus, Mar 01 2023

A093594 Farey-factorial numerators, including duplicates.

Original entry on oeis.org

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, 180, 240, 288, 360, 432, 480, 540, 576, 600, 720, 720, 840, 1008, 1260, 1440, 1680, 2016, 2160, 2520, 2880, 3024, 3360, 3600, 3780, 4032, 4200, 4320, 5040, 5040, 5760

Offset: 1

Clark Kimberling, Apr 03 2004

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.

			Put the positive Farey fractions of order n into row n,
and multiply by n!:
1
1 2
2 3 4 6
6 8 12 16 18 24 ...
Link the rows to form the sequence.

Cf. A005728, A092824, A093593.

cp's OEIS Frontend

A093593 n! times sum of Farey fractions of order n.

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