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

1,2

Links

Table of n, a(n) for n=1..22.

Eric Weisstein's World of Mathematics, Farey Sequence.

Example

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.

Mathematica

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 *)

Prog

(PARI) 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

Crossrefs

Cf. A002088, A092824, A093594.

Sequence in context: A005809 A067122 A202336 * A212201 A011900 A371754

Adjacent sequences: A093590 A093591 A093592 * A093594 A093595 A093596

Keyword

nonn

Author

Clark Kimberling, Apr 03 2004

Extensions

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

More terms from Michel Marcus, Mar 01 2023

Status

approved