A093593 -id:A093593 - cp's OEIS frontend

A093594 Farey-factorial numerators, including duplicates.

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.

A093627 a(n) = lcm(1,2,3,...,n) * (sum of Farey fractions of order n).

Original entry on oeis.org

1, 3, 15, 42, 330, 390, 3990, 9660, 36540, 41580, 595980, 651420, 10630620, 11711700, 13153140, 29189160, 594233640, 630990360, 14083949880, 15015120120, 16411875480, 17575838280, 463140798120, 484557713640, 2690500012200

Offset: 1

Robert G. Wilson v and Clark Kimberling, Apr 06 2004

nonn

Eric Weisstein's World of Mathematics, Farey Sequence.

Cf. A025527, A093593.

Farey[n_] := Union[ Flatten[ Join[{0}, Table[a/b, {b, n}, {a, b}]]]]; Table[LCM @@ Range[n] Plus @@ Farey[n], {n, 26}]

a(n) = A093593(n)/A025527(n).

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A093594 Farey-factorial numerators, including duplicates.

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A093627 a(n) = lcm(1,2,3,...,n) * (sum of Farey fractions of order n).

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