

A154888


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


4



1, 1, 2, 3, 5, 7, 11, 16, 24, 37, 48, 71, 88, 133, 284, 435, 472, 773, 826, 1835, 4369, 5546, 5649, 9924, 16465, 19944, 32324, 75913, 76168, 140802, 141141, 238514, 537697, 598296, 2556065, 4674085, 4674844, 4985386, 9716587, 23983712, 23984971
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OFFSET

1,3


COMMENTS

a(n) = A116084(n)+1 for all n because the decompositions are the same except for the additional fraction 1/1 allowed here but excluded in A116084.  M. F. Hasler, Jul 14 2016


LINKS

Table of n, a(n) for n=1..41.


EXAMPLE

a(6) = #[1, 5/6+1/6, 4/5+1/5, 3/4+1/4, 2/3+1/3, 3/5+2/5, 1/2+1/3+1/6] = 7.


MATHEMATICA

Farey[n_] := Union@ Flatten@ Table[ a/b, {b, n}, {a, b}]; t[n_, k_] := t[n, k] = Block[{c = j = 0, ip = IntegerPartitions[1, {k}, Farey@ n]}, len = 1 + Length@ ip; While[j < len, If[Plus @@ Union@ ip[[j]] == 1, c++ ]; j++ ]; c]; f[n_] := Plus @@ Table[ t[n, k], {k, Ceiling[n/2]}]; Array[f, 24] (* Robert G. Wilson v, Aug 30 2010 *)


CROSSREFS

Cf. A119983, A154887.
Equals A116084(n) + 1.
Sequence in context: A083198 A112088 A117792 * A271485 A018057 A130137
Adjacent sequences: A154885 A154886 A154887 * A154889 A154890 A154891


KEYWORD

more,nonn


AUTHOR

Reinhard Zumkeller, Jan 18 2009


EXTENSIONS

a(22)a(26) from Robert G. Wilson v, Aug 30 2010
a(27)a(34) from Don Reble, Jul 13 2016
a(35)a(41) from Giovanni Resta, Jul 15 2016


STATUS

approved



