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

Author

Ilya Gutkovskiy, Oct 28 2017

Keywords

• nonn

Examples

			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].
		

Links

• Index entries for sequences related to compositions
• Index entries for sequences related to sums of cubes

Crossrefs

Cf. A023358, A100346, A294105, A294333.

Cf. A004709, A046099.

Programs

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}]

Formula

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