A093594 -id:A093594 - 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

A118975 Triangular array: row n consists of M times n-th-order Farey fractions, where M is the LCM of their denominators.

Original entry on oeis.org

1, 1, 2, 2, 3, 4, 6, 3, 4, 6, 8, 9, 12, 12, 15, 20, 24, 30, 36, 40, 45, 48, 60, 10, 12, 15, 20, 24, 30, 36, 40, 45, 48, 50, 60, 60, 70, 84, 105, 120, 140, 168, 180, 210, 240, 252, 280, 300, 315, 336, 350, 360, 420, 105, 120, 140, 168, 210, 240

Offset: 1

Clark Kimberling, May 07 2006

The multiplier M(n) = A003418(n). Column 1 is A002944(n) = (1/n)*lcm(1,2,...,n). The numbers in row n are relatively prime (unlike the related array A093594).

			Row 4 is 12*(1/4, 1/3, 1/2, 2/3, 3/4, 1).
First 5 rows:
   1
   1  2
   2  3  4  6
   3  4  6  8  9 12
  12 15 20 24 30 36 40 45 48 60.

Cf. A003418.

cp's OEIS Frontend

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

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