A115855 Number of partitions of 1 into fractions i/j with 1<=i<j<=n and i,j coprime.

0, 1, 3, 6, 12, 21, 35, 58, 106, 188, 243, 493, 593, 1062, 3275, 5507, 5803, 12426, 12915, 42410, 131772, 167587, 168841, 428012, 839367, 1015501, 1968161, 5787286, 5791850, 15163758, 15170599, 28838712, 75983559, 82753547, 486356262, 1158442726, 1158464362

Offset

1,3

Links

Table of n, a(n) for n=1..37.

Formula

A115856(n) = a(n+1) - a(n).

Example

a(4) = #{1/2+1/2, 1/2+1/4+1/4, 1/3+2/3, 1/3+1/3+1/3, 1/4+3/4, 1/4+1/4+1/4+1/4} = 6.

Mathematica

Table[Length@ Select[Flatten[Map[IntegerPartitions[1, {#}, Rest@ Union[Flatten@ TensorProduct[#, 1/#] &@ Range@ n /. {_Integer -> 0, k_ /; k > 1 -> 0}]] &, Range@ n], 1], Total@ # == 1 &], {n, 25}] (* Michael De Vlieger, Jul 15 2016 *) (* or *)
a[n_] := Sum[ Length@ IntegerPartitions[1, {k}, Union@ Flatten[ Table[i/j, {j, n}, {i, j-1}]]], {k, n}]; Array[a, 20] (* Giovanni Resta, Jun 15 2017 *)

Crossrefs

Cf. A000041, A002966, A038566, A038567, A115856, A116084.

Sequence in context: A260640 A203292 A054578 * A234248 A294387 A128128

Adjacent sequences: A115852 A115853 A115854 * A115856 A115857 A115858

Keyword

nonn

Author

Reinhard Zumkeller, Feb 01 2006

Extensions

a(21)-a(28) from Michael De Vlieger, Jul 15 2016

More terms from Jinyuan Wang, Dec 11 2024

Status

approved