A119983 - OEIS

A119983

Number of ways to partition 1 into reduced fractions i/j with j<=n.

1, 2, 4, 7, 13, 22, 36, 59, 107, 189, 244, 494, 594, 1063, 3276, 5508, 5804, 12427, 12916, 42411, 131773, 167588, 168842, 428013, 839368, 1015502, 1968162

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OFFSET

1,2

COMMENTS

The reduced fractions are the Farey fractions of order n (A005728). - Robert G. Wilson v, Aug 30 2010

LINKS

Table of n, a(n) for n=1..27.

FORMULA

For p prime, a(p) = a(p-1) + P(p) - 1, where P is the partition function (A000041).

EXAMPLE

a(3) = 4; 1 = 1/1 = 1/2 + 1/2 = 2/3 + 1/3 = 1/3 + 1/3 + 1/3.

MATHEMATICA

Farey[n_] := Union@ Flatten@ Table[a/b, {b, n}, {a, b}]; f[n_] := Length@ IntegerPartitions[1, All, Farey@ n]; Array[f, 27] (* Robert G. Wilson v, Aug 30 2010 *)

CROSSREFS

Cf. A115855 (one less), A020473, A000041.

A154888, A154886. - Reinhard Zumkeller, Jan 17 2009

Sequence in context: A088111 A325864 A143823 * A364465 A151897 A192758

Adjacent sequences: A119980 A119981 A119982 * A119984 A119985 A119986

KEYWORD

more,nonn

AUTHOR

Franklin T. Adams-Watters, Aug 01 2006

EXTENSIONS

Definition corrected by Reinhard Zumkeller, Jan 17 2009

a(21) - a(27) from Robert G. Wilson v, Aug 30 2010

STATUS

approved