A294335 Number of compositions (ordered partitions) of n into cubes dividing n.

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 64, 1, 1, 2, 1, 1, 1, 1, 345, 1, 1, 1, 1, 1, 1, 1, 1824, 1, 1, 1, 1, 1, 1, 1, 9661, 1, 1, 1, 1, 1, 30, 1, 51284, 1, 1, 1, 1, 1, 1, 1, 272334, 1, 1, 1, 1, 1, 1, 1, 1445995, 1, 1, 1, 1, 1, 1, 1, 7677250, 463, 1, 1, 1, 1

Offset

0,9

Links

Table of n, a(n) for n=0..85.

Index entries for sequences related to compositions

Index entries for sequences related to sums of cubes

Formula

a(m)=1 when m is cubefree (A004709) and a(m)<>1 when m is not cubefree (A046099). - Michel Marcus, Oct 29 2017

Example

a(16) = 11 because 16 has 5 divisors {1, 2, 4, 8, 16} among which 2 are cubes {1, 8} therefore we have [8, 8], [8, 1, 1, 1, 1, 1, 1, 1, 1], [1, 8, 1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 1, 1, 1, 1, 1, 1], [1, 1, 1, 8, 1, 1, 1, 1, 1], [1, 1, 1, 1, 8, 1, 1, 1, 1], [1, 1, 1, 1, 1, 8, 1, 1, 1], [1, 1, 1, 1, 1, 1, 8, 1, 1], [1, 1, 1, 1, 1, 1, 1, 8, 1], [1, 1, 1, 1, 1, 1, 1, 1, 8] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1].

Mathematica

Table[SeriesCoefficient[1/(1 - Sum[Boole[Mod[n, k] == 0 && IntegerQ[k^(1/3)]] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 85}]

Crossrefs

Cf. A023358, A100346, A294105, A294333.

Cf. A004709, A046099.

Sequence in context: A078090 A174341 A168516 * A194321 A194852 A158854

Adjacent sequences: A294332 A294333 A294334 * A294336 A294337 A294338

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 28 2017

Status

approved