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A119983
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Number of ways to partition 1 into reduced fractions i/j with j<=n.
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3
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The reduced fractions are the Farey fractions of order n (A005728). [From Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 30 2010]
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FORMULA
| For p prime, a(p) = a(p-1) + P(p) - 1, where P is the partition function (A000041).
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EXAMPLE
| a(3) = 4; 1 = 1/1 = 1/2 + 1/2 = 2/3 + 1/3 = 1/3 + 1/3 + 1/3.
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MATHEMATICA
| Farey[n_] := Union@ Flatten@ Table[a/b, {b, n}, {a, b}]; f[n_] := Length@ IntegerPartitions[1, All, Farey@ n]; Array[f, 27] [From Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 30 2010]
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CROSSREFS
| Cf. A115855 (one less), A020473, A000041.
A154888, A154886. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 17 2009]
Sequence in context: A061255 A088111 A143823 * A151897 A192758 A085489
Adjacent sequences: A119980 A119981 A119982 * A119984 A119985 A119986
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KEYWORD
| more,nonn
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AUTHOR
| Frank Adams-Watters (FrankTAW(AT)Netscape.net), Aug 01 2006
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EXTENSIONS
| Definition corrected by Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 17 2009
a(21) - a(27) from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 30 2010
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